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2026-01-01
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<p>Last updated on<strong>November 1, 2025</strong></p>
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<p>Last updated on<strong>November 1, 2025</strong></p>
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<p>Matrices are divided into different types based on their elements, size, and special properties. The word ‘matrices’ is simply the plural form of ‘matrix’, which refers to an arrangement of numbers organized in rows and columns.</p>
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<p>Matrices are divided into different types based on their elements, size, and special properties. The word ‘matrices’ is simply the plural form of ‘matrix’, which refers to an arrangement of numbers organized in rows and columns.</p>
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<h2>What are the Types of Matrices?</h2>
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<h2>What are the Types of Matrices?</h2>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>▶</p>
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<p>The type<a>of</a>matrix depends on its components, size, and<a>number</a>of rows and columns. This section discusses how different types of matrices are categorized.</p>
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<p>The type<a>of</a>matrix depends on its components, size, and<a>number</a>of rows and columns. This section discusses how different types of matrices are categorized.</p>
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<h3>Row Matrix</h3>
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<h3>Row Matrix</h3>
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<p>A matrix with just one row and any number of columns is a<a>row matrix</a>. Here, the number of columns doesn’t matter, but the matrix will always have just one row. Thus, A = [aij]1n is a row matrix if m = 1. The elements are written horizontally like a list. So, a row matrix is represented as:</p>
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<p>A matrix with just one row and any number of columns is a<a>row matrix</a>. Here, the number of columns doesn’t matter, but the matrix will always have just one row. Thus, A = [aij]1n is a row matrix if m = 1. The elements are written horizontally like a list. So, a row matrix is represented as:</p>
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<p>A = [a11 a12 a13 … a1n]1n</p>
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<p>A = [a11 a12 a13 … a1n]1n</p>
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<p><strong>Example:</strong></p>
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<p><strong>Example:</strong></p>
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<p>A = [1 2] is a 1 × 2 row matrix.</p>
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<p>A = [1 2] is a 1 × 2 row matrix.</p>
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<p>B = [3 2 1] is a 1 × 3 row matrix.</p>
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<p>B = [3 2 1] is a 1 × 3 row matrix.</p>
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<p>C = [2 3 4 5] is a 1 × 4 row matrix.</p>
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<p>C = [2 3 4 5] is a 1 × 4 row matrix.</p>
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<h2><strong>Properties of Row Matrix</strong></h2>
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<h2><strong>Properties of Row Matrix</strong></h2>
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<ul><li>A row matrix has a single row. </li>
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<ul><li>A row matrix has a single row. </li>
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<li>A row matrix has many columns. </li>
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<li>A row matrix has many columns. </li>
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<li>In a row matrix, since all the elements are in a single row, the number of columns equals the number of elements.</li>
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<li>In a row matrix, since all the elements are in a single row, the number of columns equals the number of elements.</li>
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</ul><h2>Column Matrix</h2>
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</ul><h2>Column Matrix</h2>
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<p>A column matrix has only one column and any number of rows. If n = 1, then A = [aij]m1 is a column matrix. The elements are arranged vertically with m rows and 1 column.</p>
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<p>A column matrix has only one column and any number of rows. If n = 1, then A = [aij]m1 is a column matrix. The elements are arranged vertically with m rows and 1 column.</p>
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<h2><strong> Properties of Column Matrix</strong></h2>
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<h2><strong> Properties of Column Matrix</strong></h2>
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<ul><li><p>A column matrix has a single column.</p>
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<ul><li><p>A column matrix has a single column.</p>
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</li>
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</li>
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<li>A column matrix has many rows. </li>
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<li>A column matrix has many rows. </li>
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<li>Since there is only one column, the number of elements is equal to the number of rows.</li>
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<li>Since there is only one column, the number of elements is equal to the number of rows.</li>
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</ul><h3>Explore Our Programs</h3>
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</ul><h3>Explore Our Programs</h3>
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<h3>Zero or Null Matrix</h3>
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<h3>Zero or Null Matrix</h3>
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<p>A null matrix is a matrix where every element is zero. Therefore, it is also known as a zero matrix. A null matrix is of the order m n, depending on how many rows and columns it has. It is represented as A = [aij]mn, where aij = 0 for all<a>i</a>and j. </p>
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<p>A null matrix is a matrix where every element is zero. Therefore, it is also known as a zero matrix. A null matrix is of the order m n, depending on how many rows and columns it has. It is represented as A = [aij]mn, where aij = 0 for all<a>i</a>and j. </p>
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<h2><strong>Properties Of Zero Matrix (Null Matrix)</strong></h2>
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<h2><strong>Properties Of Zero Matrix (Null Matrix)</strong></h2>
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<ul><li>The null matrix<strong></strong>can either be<a>square</a>or rectangular, depending on the number of rows and columns. </li>
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<ul><li>The null matrix<strong></strong>can either be<a>square</a>or rectangular, depending on the number of rows and columns. </li>
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<li>This null matrix can have an unequal number of rows and columns. </li>
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<li>This null matrix can have an unequal number of rows and columns. </li>
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<li>A null matrix is always singular because its<a>determinant</a>is zero (for square matrices), and it doesn’t have an inverse.</li>
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<li>A null matrix is always singular because its<a>determinant</a>is zero (for square matrices), and it doesn’t have an inverse.</li>
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</ul><h3>Singleton Matrix</h3>
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</ul><h3>Singleton Matrix</h3>
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<p>A singleton matrix contains only one element. It has one row and one column, so its order is 1 1. </p>
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<p>A singleton matrix contains only one element. It has one row and one column, so its order is 1 1. </p>
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<p><strong>Properties of Singleton Matrix</strong></p>
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<p><strong>Properties of Singleton Matrix</strong></p>
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<ul><li>It has only one row and one column. </li>
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<ul><li>It has only one row and one column. </li>
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<li>A singleton matrix contains only one element. </li>
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<li>A singleton matrix contains only one element. </li>
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<li>All singleton matrices are square matrices.</li>
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<li>All singleton matrices are square matrices.</li>
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</ul><h3>Horizontal Matrix</h3>
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</ul><h3>Horizontal Matrix</h3>
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<p>A horizontal matrix or row matrix has only one row and any number of columns. Thus, it is represented as [aij]mn. It has the order of</p>
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<p>A horizontal matrix or row matrix has only one row and any number of columns. Thus, it is represented as [aij]mn. It has the order of</p>
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<p> m × n.</p>
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<p> m × n.</p>
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<p> A = [p q r s]</p>
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<p> A = [p q r s]</p>
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<p> Example:</p>
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<p> Example:</p>
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<p>A = [2 2 5 8] is a horizontal matrix of the order 1 × 4.</p>
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<p>A = [2 2 5 8] is a horizontal matrix of the order 1 × 4.</p>
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<p><strong>Properties of Horizontal Matrix</strong></p>
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<p><strong>Properties of Horizontal Matrix</strong></p>
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<ul><li>It has more columns than rows. </li>
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<ul><li>It has more columns than rows. </li>
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<li>It has only a single row. </li>
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<li>It has only a single row. </li>
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<li>It is also known as Row Matrix.</li>
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<li>It is also known as Row Matrix.</li>
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</ul><h3>Vertical Matrix</h3>
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</ul><h3>Vertical Matrix</h3>
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<p>It is the matrix in which the number of rows exceeds the number of columns. Thus, it is represented as [aij]mn</p>
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<p>It is the matrix in which the number of rows exceeds the number of columns. Thus, it is represented as [aij]mn</p>
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<p><strong>Properties of Vertical Matrix</strong></p>
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<p><strong>Properties of Vertical Matrix</strong></p>
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<ul><li>It has more rows than columns. </li>
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<ul><li>It has more rows than columns. </li>
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<li>If it has only one column, then it is called a column matrix. </li>
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<li>If it has only one column, then it is called a column matrix. </li>
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<li>It is not square if the number of rows is<a>not equal</a>to the number of columns.</li>
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<li>It is not square if the number of rows is<a>not equal</a>to the number of columns.</li>
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</ul><h3>Square Matrix</h3>
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</ul><h3>Square Matrix</h3>
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<p>A square matrix has an equal number of rows and columns. Thus, it is represented as [aij]mn. It is of the order m × n, where m = n. </p>
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<p>A square matrix has an equal number of rows and columns. Thus, it is represented as [aij]mn. It is of the order m × n, where m = n. </p>
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<p><strong>Properties of Square Matrix</strong></p>
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<p><strong>Properties of Square Matrix</strong></p>
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<ul><li>The number of rows and columns is the same. </li>
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<ul><li>The number of rows and columns is the same. </li>
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<li>Only square matrices have a determinant. </li>
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<li>Only square matrices have a determinant. </li>
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<li>Its transpose is also a square matrix.</li>
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<li>Its transpose is also a square matrix.</li>
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</ul><h3>Diagonal Matrix</h3>
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</ul><h3>Diagonal Matrix</h3>
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<p>A diagonal matrix is a square matrix with zero values for every element outside the main diagonal. It is therefore expressed as A = [aij]. Only the main diagonal contains non-zero elements.</p>
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<p>A diagonal matrix is a square matrix with zero values for every element outside the main diagonal. It is therefore expressed as A = [aij]. Only the main diagonal contains non-zero elements.</p>
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<p><strong>Properties of a Diagonal Matrix</strong></p>
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<p><strong>Properties of a Diagonal Matrix</strong></p>
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<ul><li>Every diagonal matrix is a square matrix. </li>
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<ul><li>Every diagonal matrix is a square matrix. </li>
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<li>The number of rows in a diagonal matrix is equal to the number of columns. </li>
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<li>The number of rows in a diagonal matrix is equal to the number of columns. </li>
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<li>The<a>sum</a>of two diagonal matrices results in another diagonal matrix.</li>
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<li>The<a>sum</a>of two diagonal matrices results in another diagonal matrix.</li>
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</ul><h3>Scalar Matrix</h3>
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</ul><h3>Scalar Matrix</h3>
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<p>A Scalar matrix is a square matrix in which all the elements of the principal diagonal are the same and all other elements are zero. Therefore, it is written as A = [aij]mn</p>
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<p>A Scalar matrix is a square matrix in which all the elements of the principal diagonal are the same and all other elements are zero. Therefore, it is written as A = [aij]mn</p>
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<p> <strong>Properties of Scalar Matrix</strong></p>
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<p> <strong>Properties of Scalar Matrix</strong></p>
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<ul><li>All the numbers outside the main diagonal are zero. </li>
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<ul><li>All the numbers outside the main diagonal are zero. </li>
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<li>The determinant of a scalar matrix is equal to the scalar value raised to the<a>power</a>of the order of the matrix. </li>
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<li>The determinant of a scalar matrix is equal to the scalar value raised to the<a>power</a>of the order of the matrix. </li>
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<li>It is a special type of square matrix where all the diagonal elements are equal, and all off-diagonal elements are zero.</li>
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<li>It is a special type of square matrix where all the diagonal elements are equal, and all off-diagonal elements are zero.</li>
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</ul><h3>Identity (Unit) Matrix</h3>
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</ul><h3>Identity (Unit) Matrix</h3>
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<p>An<a>identity matrix</a>is a square matrix with ones on the main diagonal and zero elsewhere. Thus, it is represented as A = [aij]mn. The identity matrix works like the number 1 in<a>multiplication</a>, when any square matrix is multiplied by it, the result is the original matrix value.</p>
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<p>An<a>identity matrix</a>is a square matrix with ones on the main diagonal and zero elsewhere. Thus, it is represented as A = [aij]mn. The identity matrix works like the number 1 in<a>multiplication</a>, when any square matrix is multiplied by it, the result is the original matrix value.</p>
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<p>For any matrix A of order n × n, AI = IA = A</p>
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<p>For any matrix A of order n × n, AI = IA = A</p>
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<p><strong>Properties of Identity Matrix</strong></p>
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<p><strong>Properties of Identity Matrix</strong></p>
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<ul><li>The identity matrix is always square. </li>
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<ul><li>The identity matrix is always square. </li>
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<li>A matrix remains unchanged when it’s multiplied by the identity matrix. </li>
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<li>A matrix remains unchanged when it’s multiplied by the identity matrix. </li>
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<li>The determinant is always 1.</li>
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<li>The determinant is always 1.</li>
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</ul><h3>Equal Matrix</h3>
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</ul><h3>Equal Matrix</h3>
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<p>When two matrices have the same dimensions, they are considered equal. Thus, it is represented as A = [aij]mn and B = [bij]rs. A and B are equal only if m = r, n = s, and aij = bij for all i, j. </p>
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<p>When two matrices have the same dimensions, they are considered equal. Thus, it is represented as A = [aij]mn and B = [bij]rs. A and B are equal only if m = r, n = s, and aij = bij for all i, j. </p>
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<p><strong>Properties of Equal Matrix</strong></p>
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<p><strong>Properties of Equal Matrix</strong></p>
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<ul><li>Two matrices are equal if they have the same size. </li>
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<ul><li>Two matrices are equal if they have the same size. </li>
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<li>Even if one element is different, the matrices are not equal. </li>
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<li>Even if one element is different, the matrices are not equal. </li>
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<li>The matrices can be compared for equality only when their orders<a>match</a>exactly.</li>
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<li>The matrices can be compared for equality only when their orders<a>match</a>exactly.</li>
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</ul><h3>Triangular Matrix</h3>
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</ul><h3>Triangular Matrix</h3>
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<p>A<a>triangular matrix</a>is a special type of square matrix. Here, all the elements found above or below the main diagonal are zeros.</p>
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<p>A<a>triangular matrix</a>is a special type of square matrix. Here, all the elements found above or below the main diagonal are zeros.</p>
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<p><strong>Properties of Triangular Matrix</strong></p>
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<p><strong>Properties of Triangular Matrix</strong></p>
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<ul><li>The inverse of a triangular matrix (if it exists) will also be triangular. </li>
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<ul><li>The inverse of a triangular matrix (if it exists) will also be triangular. </li>
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<li>The determinant of a triangular matrix is found by multiplying all the diagonal values together. </li>
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<li>The determinant of a triangular matrix is found by multiplying all the diagonal values together. </li>
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<li>A triangular matrix can only be inverted if none of the diagonal elements are zero.</li>
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<li>A triangular matrix can only be inverted if none of the diagonal elements are zero.</li>
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</ul><h3>Singular Matrix</h3>
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</ul><h3>Singular Matrix</h3>
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<p>A<a>singular matrix</a>is a square matrix whose determinant is equal to zero.</p>
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<p>A<a>singular matrix</a>is a square matrix whose determinant is equal to zero.</p>
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<p>It is represented as |A|=0.</p>
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<p>It is represented as |A|=0.</p>
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<p><strong>Properties of Singular Matrix</strong></p>
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<p><strong>Properties of Singular Matrix</strong></p>
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<ul><li>A matrix is called singular when its determinant turns out to be zero, making it non-invertible. </li>
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<ul><li>A matrix is called singular when its determinant turns out to be zero, making it non-invertible. </li>
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<li>Since its determinant is zero, a singular matrix doesn’t have an inverse. </li>
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<li>Since its determinant is zero, a singular matrix doesn’t have an inverse. </li>
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<li>A zero matrix is always singular because its determinant is zero.</li>
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<li>A zero matrix is always singular because its determinant is zero.</li>
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</ul><h3>Non-Singular Matrix</h3>
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</ul><h3>Non-Singular Matrix</h3>
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<p>A matrix is called non-singular if it has an inverse. In other words, it must be square, and its determinant must not be zero.</p>
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<p>A matrix is called non-singular if it has an inverse. In other words, it must be square, and its determinant must not be zero.</p>
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<p>It can be represented as |A| ≠ 0.</p>
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<p>It can be represented as |A| ≠ 0.</p>
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<p> <strong>Properties of Non-singular Matrix</strong></p>
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<p> <strong>Properties of Non-singular Matrix</strong></p>
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<ul><li>A<a>non-singular matrix</a>has a non-zero determinant - but not every non-zero matrix is non-singular. </li>
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<ul><li>A<a>non-singular matrix</a>has a non-zero determinant - but not every non-zero matrix is non-singular. </li>
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<li>A matrix must have the same number of rows and columns to qualify as non-singular. </li>
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<li>A matrix must have the same number of rows and columns to qualify as non-singular. </li>
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<li>A non-singular matrix always has an inverse.</li>
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<li>A non-singular matrix always has an inverse.</li>
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</ul><h3>Symmetric Matrices</h3>
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</ul><h3>Symmetric Matrices</h3>
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<p>A<a>symmetric matrix</a>is a square matrix where elements are mirrored across the main diagonal - in other words, the entry in row<em>i</em>, column<em>j</em>is equal to the entry in row<em>j</em>, column<em>i</em>.</p>
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<p>A<a>symmetric matrix</a>is a square matrix where elements are mirrored across the main diagonal - in other words, the entry in row<em>i</em>, column<em>j</em>is equal to the entry in row<em>j</em>, column<em>i</em>.</p>
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<p><strong>Properties of Symmetric Matrices</strong></p>
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<p><strong>Properties of Symmetric Matrices</strong></p>
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<ul><li>A symmetric matrix can be diagonalized using an orthogonal transformation. </li>
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<ul><li>A symmetric matrix can be diagonalized using an orthogonal transformation. </li>
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<li>It has real<a>eigenvalues</a>. </li>
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<li>It has real<a>eigenvalues</a>. </li>
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<li>When two symmetric matrices are added or subtracted, the result is also a symmetric matrix.</li>
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<li>When two symmetric matrices are added or subtracted, the result is also a symmetric matrix.</li>
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</ul><h3>Skew Symmetric Matrices</h3>
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</ul><h3>Skew Symmetric Matrices</h3>
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<p>It is a square matrix where the transpose is equal to the negative of the original matrix.</p>
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<p>It is a square matrix where the transpose is equal to the negative of the original matrix.</p>
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<p>It is represented as A=[aij].</p>
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<p>It is represented as A=[aij].</p>
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<p><strong>Properties of Skew-Symmetric Matrix</strong></p>
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<p><strong>Properties of Skew-Symmetric Matrix</strong></p>
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<ul><li>In a skew-symmetric matrix, the sum of the diagonal elements is zero. </li>
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<ul><li>In a skew-symmetric matrix, the sum of the diagonal elements is zero. </li>
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<li>When a real skew-symmetric matrix is added to the identity matrix, the result will be non-singular. </li>
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<li>When a real skew-symmetric matrix is added to the identity matrix, the result will be non-singular. </li>
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<li>When a skew-symmetric matrix is squared, the result will be symmetric.</li>
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<li>When a skew-symmetric matrix is squared, the result will be symmetric.</li>
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</ul><h3>Hermitian Matrix</h3>
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</ul><h3>Hermitian Matrix</h3>
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<p>It is a square matrix made up of<a>complex numbers</a>, where the matrix is equal to its own<a>conjugate</a>transpose. </p>
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<p>It is a square matrix made up of<a>complex numbers</a>, where the matrix is equal to its own<a>conjugate</a>transpose. </p>
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<p>It is represented as A=A*.</p>
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<p>It is represented as A=A*.</p>
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<p><strong>Properties of Hermitian Matrix</strong></p>
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<p><strong>Properties of Hermitian Matrix</strong></p>
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<ul><li>Every Hermitian matrix is a normal matrix. </li>
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<ul><li>Every Hermitian matrix is a normal matrix. </li>
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<li>The sum of two Hermitian matrices is also Hermitian. </li>
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<li>The sum of two Hermitian matrices is also Hermitian. </li>
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<li>If a Hermitian matrix is non-singular, its inverse is also Hermitian.</li>
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<li>If a Hermitian matrix is non-singular, its inverse is also Hermitian.</li>
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</ul><h3>Skew Hermitian Matrix</h3>
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</ul><h3>Skew Hermitian Matrix</h3>
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<p>It is a square matrix with complex entries, where the conjugate transpose is equal to the negative of the original matrix<strong>.</strong></p>
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<p>It is a square matrix with complex entries, where the conjugate transpose is equal to the negative of the original matrix<strong>.</strong></p>
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<p>It is represented as A* = -A.</p>
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<p>It is represented as A* = -A.</p>
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<p><strong>Properties of Skew Hermitian Matrix</strong></p>
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<p><strong>Properties of Skew Hermitian Matrix</strong></p>
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<ul><li>A skew Hermitian matrix can be diagonalized. </li>
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<ul><li>A skew Hermitian matrix can be diagonalized. </li>
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<li>Its eigenvalues are always purely imaginary or zero. </li>
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<li>Its eigenvalues are always purely imaginary or zero. </li>
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<li>When a skew Hermitian matrix is multiplied by a scalar, then the result will be skew Hermitian.</li>
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<li>When a skew Hermitian matrix is multiplied by a scalar, then the result will be skew Hermitian.</li>
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</ul><h3>Orthogonal Matrix</h3>
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</ul><h3>Orthogonal Matrix</h3>
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<p>An<a>orthogonal matrix</a>is a square matrix with real entries whose rows and columns are orthonormal vectors. It is represented as AAᵀ =I=AᵀA.</p>
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<p>An<a>orthogonal matrix</a>is a square matrix with real entries whose rows and columns are orthonormal vectors. It is represented as AAᵀ =I=AᵀA.</p>
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<p><strong>Properties of Orthogonal Matrix</strong></p>
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<p><strong>Properties of Orthogonal Matrix</strong></p>
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<ul><li>The inverse of an orthogonal matrix is equal to its transpose. </li>
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<ul><li>The inverse of an orthogonal matrix is equal to its transpose. </li>
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<li>Multiplying any vector by an orthogonal matrix does not change the vector’s length or the angle between vectors. </li>
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<li>Multiplying any vector by an orthogonal matrix does not change the vector’s length or the angle between vectors. </li>
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<li>Its eigenvalues are either +1 or -1 and<a>eigenvectors</a>are orthogonal.</li>
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<li>Its eigenvalues are either +1 or -1 and<a>eigenvectors</a>are orthogonal.</li>
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</ul><h3>Idempotent Matrix</h3>
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</ul><h3>Idempotent Matrix</h3>
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<p>A square matrix that yields the same matrix when multiplied by itself is called an idempotent matrix.</p>
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<p>A square matrix that yields the same matrix when multiplied by itself is called an idempotent matrix.</p>
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<p>It is represented as A2=A.</p>
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<p>It is represented as A2=A.</p>
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<p><strong>Properties of Idempotent Matrix</strong></p>
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<p><strong>Properties of Idempotent Matrix</strong></p>
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<ul><li>An idempotent matrix is always a square matrix. </li>
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<ul><li>An idempotent matrix is always a square matrix. </li>
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<li>It has the same number of rows and columns, making it a square matrix. </li>
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<li>It has the same number of rows and columns, making it a square matrix. </li>
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<li>If the determinant of an idempotent matrix is zero, it is typically singular.</li>
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<li>If the determinant of an idempotent matrix is zero, it is typically singular.</li>
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</ul><h3>Involutory Matrix</h3>
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</ul><h3>Involutory Matrix</h3>
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<p>An<a>involutory matrix</a>is a square matrix that gives the identity matrix when multiplied by itself. It is represented as A2 =I,A-1=A.</p>
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<p>An<a>involutory matrix</a>is a square matrix that gives the identity matrix when multiplied by itself. It is represented as A2 =I,A-1=A.</p>
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<p><strong>Properties of Involutory Matrix</strong></p>
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<p><strong>Properties of Involutory Matrix</strong></p>
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<ul><li>When a block diagonal matrix is created using an involutory matrix, the result will also be involutory. </li>
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<ul><li>When a block diagonal matrix is created using an involutory matrix, the result will also be involutory. </li>
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<li>The eigenvalues of an involutory matrix are always either +1 or -1. </li>
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<li>The eigenvalues of an involutory matrix are always either +1 or -1. </li>
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<li>The determinant of an involutory matrix is always +1 or -1.</li>
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<li>The determinant of an involutory matrix is always +1 or -1.</li>
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</ul><h3>Nilpotent Matrix</h3>
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</ul><h3>Nilpotent Matrix</h3>
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<p>A square matrix that yields a zero matrix for a<a>positive integer</a>power is called a<a>nilpotent matrix</a>.</p>
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<p>A square matrix that yields a zero matrix for a<a>positive integer</a>power is called a<a>nilpotent matrix</a>.</p>
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<p>It is represented as Ap =0.</p>
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<p>It is represented as Ap =0.</p>
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<p><strong>Properties of Nilpotent Matrix</strong></p>
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<p><strong>Properties of Nilpotent Matrix</strong></p>
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<ul><li>The only diagonalizable nilpotent matrix is the zero matrix. </li>
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<ul><li>The only diagonalizable nilpotent matrix is the zero matrix. </li>
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<li>A triangular matrix is said to be nilpotent if its principal diagonal contains all zeros. </li>
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<li>A triangular matrix is said to be nilpotent if its principal diagonal contains all zeros. </li>
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<li>A nilpotent matrix is singular, since its determinant is always equal to zero.</li>
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<li>A nilpotent matrix is singular, since its determinant is always equal to zero.</li>
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</ul><h2>Common Mistakes and How to Avoid Them in Types of Matrices</h2>
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</ul><h2>Common Mistakes and How to Avoid Them in Types of Matrices</h2>
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<p>Students can get confused with the different types of matrices, which could lead to mistakes. Knowing some of these mistakes beforehand will help us avoid similar mistakes while dealing with different kinds of matrices.</p>
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<p>Students can get confused with the different types of matrices, which could lead to mistakes. Knowing some of these mistakes beforehand will help us avoid similar mistakes while dealing with different kinds of matrices.</p>
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<h2>Real World Applications of Types of Matrices</h2>
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<h2>Real World Applications of Types of Matrices</h2>
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<p>Matrices have wide applications in various fields. Here, we will discuss some of those real-life applications.</p>
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<p>Matrices have wide applications in various fields. Here, we will discuss some of those real-life applications.</p>
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<ol><li><strong>Computer Graphics</strong></li>
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<ol><li><strong>Computer Graphics</strong></li>
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</ol><p>Matrices help make simulations, video games, and animations in computer graphics look more realistic and lifelike.</p>
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</ol><p>Matrices help make simulations, video games, and animations in computer graphics look more realistic and lifelike.</p>
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<ol><li><strong>Engineering and Physics</strong></li>
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<ol><li><strong>Engineering and Physics</strong></li>
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</ol><p>Complex problems, such as determining how forces act on a bridge, how electricity flows through circuits, or how heat moves through materials, can be solved with the help of matrices.</p>
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</ol><p>Complex problems, such as determining how forces act on a bridge, how electricity flows through circuits, or how heat moves through materials, can be solved with the help of matrices.</p>
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<ol><li><strong>Cryptography</strong></li>
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<ol><li><strong>Cryptography</strong></li>
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</ol><p>They contribute to the security of information. When you send secure messages or do online banking, matrices help encrypt<a>data</a>for security reasons.</p>
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</ol><p>They contribute to the security of information. When you send secure messages or do online banking, matrices help encrypt<a>data</a>for security reasons.</p>
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<ol><li><strong>Data Science and Machine Learning</strong></li>
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<ol><li><strong>Data Science and Machine Learning</strong></li>
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</ol><p>Matrices help process large amounts of data efficiently. They also play a key role in computer decision-making within AI models like neural networks.</p>
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</ol><p>Matrices help process large amounts of data efficiently. They also play a key role in computer decision-making within AI models like neural networks.</p>
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<ol><li><strong>Computer Vision</strong></li>
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<ol><li><strong>Computer Vision</strong></li>
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</ol><p>Images are stored as number grids, just like matrices. Computers use these grids to sharpen pictures, recognize faces, and even help doctors spot health problems in medical scans.</p>
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</ol><p>Images are stored as number grids, just like matrices. Computers use these grids to sharpen pictures, recognize faces, and even help doctors spot health problems in medical scans.</p>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>A=[43 51 ],B=[23 2-1 ] Calculate A + B</p>
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<p>A=[43 51 ],B=[23 2-1 ] Calculate A + B</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>\(A + B = \begin{bmatrix} 6 & 7 \\ 6 & 0 \end{bmatrix}\)</p>
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<p>\(A + B = \begin{bmatrix} 6 & 7 \\ 6 & 0 \end{bmatrix}\)</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>\(A = \begin{bmatrix} 4 & 5 \\ 3 & 1 \end{bmatrix}\) \(B = \begin{bmatrix} 2 & 2 \\ 3 & -1 \end{bmatrix} \)</p>
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<p>\(A = \begin{bmatrix} 4 & 5 \\ 3 & 1 \end{bmatrix}\) \(B = \begin{bmatrix} 2 & 2 \\ 3 & -1 \end{bmatrix} \)</p>
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<p>\(A + B = \begin{bmatrix} 4+2 & 5+2 \\ 3+3 & 1+(-1) \end{bmatrix}\)</p>
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<p>\(A + B = \begin{bmatrix} 4+2 & 5+2 \\ 3+3 & 1+(-1) \end{bmatrix}\)</p>
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<p>\(A + B = \begin{bmatrix} 6 & 7 \\ 6 & 0 \end{bmatrix}\)</p>
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<p>\(A + B = \begin{bmatrix} 6 & 7 \\ 6 & 0 \end{bmatrix}\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A = \begin{bmatrix} 2 & 2 \\ 0 & -1 \end{bmatrix} Find the inverse of a matrix.</p>
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<p>A = \begin{bmatrix} 2 & 2 \\ 0 & -1 \end{bmatrix} Find the inverse of a matrix.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>\(A^{-1} = \begin{bmatrix} \frac{1}{2} & 1 \\ 0 & -1 \end{bmatrix}\)</p>
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<p>\(A^{-1} = \begin{bmatrix} \frac{1}{2} & 1 \\ 0 & -1 \end{bmatrix}\)</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>\(\text{Let } A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)</p>
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<p>\(\text{Let } A = \begin{bmatrix} a & b \\ c & d \end{bmatrix}\)</p>
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<p>The inverse of A is: \(A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)</p>
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<p>The inverse of A is: \(A^{-1} = \frac{1}{ad - bc} \begin{bmatrix} d & -b \\ -c & a \end{bmatrix}\)</p>
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<p>Here Let us know the values </p>
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<p>Here Let us know the values </p>
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<p>a = 2</p>
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<p>a = 2</p>
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<p>b = 0</p>
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<p>b = 0</p>
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<p>c = 2 </p>
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<p>c = 2 </p>
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<p>d = -1</p>
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<p>d = -1</p>
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<p>\(\text{Det}(A) = ad - bc = (2)(-1) - (2)(0) = -2\)</p>
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<p>\(\text{Det}(A) = ad - bc = (2)(-1) - (2)(0) = -2\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>Prove that the product of the matrices and the identity matrix of order 3 × 3 is the matrix itself. A = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}</p>
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<p>Prove that the product of the matrices and the identity matrix of order 3 × 3 is the matrix itself. A = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}\)</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}\)</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>\(I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) It is the identity matrix</p>
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<p>\(I = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) It is the identity matrix</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix} \times \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\)</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix} \times \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}\)</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}\)</p>
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<p>\(A \times I = \begin{bmatrix} 2 & 3 & -2 \\ 5 & 1 & 0 \\ -4 & 0 & 2 \end{bmatrix}\)</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>A = \begin{bmatrix} 2 & 5 \\ 1 & 0 \end{bmatrix} Find the determinant of the following.</p>
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<p>A = \begin{bmatrix} 2 & 5 \\ 1 & 0 \end{bmatrix} Find the determinant of the following.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Determinant of A = -5</p>
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<p>Determinant of A = -5</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Det (A) = ad - bc</p>
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<p>Det (A) = ad - bc</p>
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<p>Now let us know the values,</p>
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<p>Now let us know the values,</p>
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<ul><li>a = 2</li>
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<ul><li>a = 2</li>
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<li>b = 5</li>
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<li>b = 5</li>
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<li>c = 1</li>
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<li>c = 1</li>
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<li>d = 0</li>
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<li>d = 0</li>
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</ul><p>Let us solve,</p>
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</ul><p>Let us solve,</p>
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<p>Det (A) = (2 × 0) - (5 × 1) </p>
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<p>Det (A) = (2 × 0) - (5 × 1) </p>
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<p> = 0 - 5</p>
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<p> = 0 - 5</p>
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<p> = - 5</p>
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<p> = - 5</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>A = \begin{bmatrix} 1 & 5 \\ 1 & -2 \end{bmatrix} Determine the matrix’s transpose.</p>
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<p>A = \begin{bmatrix} 1 & 5 \\ 1 & -2 \end{bmatrix} Determine the matrix’s transpose.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>\(A^{T} = \begin{bmatrix} 1 & 1 \\ 5 & -2 \end{bmatrix}\)</p>
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<p>\(A^{T} = \begin{bmatrix} 1 & 1 \\ 5 & -2 \end{bmatrix}\)</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the transpose of a matrix, swap its rows with columns.</p>
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<p>To find the transpose of a matrix, swap its rows with columns.</p>
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<p>(i, j) becomes (j, i).</p>
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<p>(i, j) becomes (j, i).</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on Types of Matrices</h2>
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<h2>FAQs on Types of Matrices</h2>
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<h3>1.What is a matrix?</h3>
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<h3>1.What is a matrix?</h3>
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<p>A grid of numbers with rows and columns is called a matrix.</p>
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<p>A grid of numbers with rows and columns is called a matrix.</p>
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<h3>2.What is the order of the matrix?</h3>
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<h3>2.What is the order of the matrix?</h3>
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<p>The order of the matrix refers to its dimensions, i.e., rows and columns.</p>
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<p>The order of the matrix refers to its dimensions, i.e., rows and columns.</p>
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<h3>3.What is a square matrix?</h3>
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<h3>3.What is a square matrix?</h3>
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<p>A matrix having equal number of rows and columns is a square matrix.</p>
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<p>A matrix having equal number of rows and columns is a square matrix.</p>
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<h3>4.What is an Identity matrix?</h3>
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<h3>4.What is an Identity matrix?</h3>
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<p>A square matrix in which all the elements of the principal diagonals are 1 and all other elements are 0.</p>
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<p>A square matrix in which all the elements of the principal diagonals are 1 and all other elements are 0.</p>
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<h3>5.How many kinds of matrices are there?</h3>
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<h3>5.How many kinds of matrices are there?</h3>
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<p>There are over 15 different kinds of matrices.</p>
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<p>There are over 15 different kinds of matrices.</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>