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2 <p>Last updated on<strong>December 10, 2025</strong></p>

3 <p>A symmetric matrix is a square matrix which remains the same even after transposed, i.e., A = AT. In this article, we will be discussing the symmetric matrix.</p>

4 <h2>What is a Matrix?</h2>

5 <p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

6 <p>▶</p>

7 <p>A matrix is a rectangular array of<a>numbers</a>arranged in rows and columns. Matrices are used to represent linear transformations, perform matrix operations, and solve systems of<a>linear equations</a>. A matrix with ‘m’ rows and ‘n’ columns is denoted as m × n. A<a>square</a>matrix has equal numbers of rows and columns, n × n. </p>

8 <h2>What is a Symmetric Matrix?</h2>

9 <p>A<a>symmetric matrix</a>satisfies the condition A = AT, i.e., the matrix and its transpose are equal. This suggests that it must be a square matrix, and each element in the (i, j) position must equal the elements in the position (j, i). i.e., aij = aji. </p>

10 <p>For example, </p>

11 <p>\( \begin{bmatrix} 2 & 3 & 4 \\ 3 & 5 & 6 \\ 4 & 6 & 7 \end{bmatrix} \)</p>

12 <p>This is a symmetric matrix.</p>

13 <h2>Difference Between Skew-Symmetric and Symmetric Matrix</h2>

14 <p>Skew-symmetry is a property of square matrices. It is different from a symmetric matrix in the following ways: </p>

15 <p><strong>Symmetric matrix</strong></p>

16 <p><strong>Skew-symmetric matrix</strong></p>

17 <p> A symmetric matrix is a square matrix with mirrored elements across the main diagonal. Mathematically, a matrix A is symmetric if A = AT. Here, AT is the transpose.</p>

18 <p>A skew-symmetric matrix is a square matrix in which the transpose of the matrix equals the negative of the original matrix. This is mathematically represented as A = -AT</p>

19 <p>Each element satisfies aij = aji</p>

20 <p>Each element satisfies aij = - aji</p>

21 <p>The diagonal elements can be any<a>real numbers</a>. </p>

22 <p>All diagonal elements are zero.</p>

23 <p>The<a>sum</a>of a symmetric matrix and its transpose is A + AT = 2A.</p>

24 <p>The sum with its transpose for a skew-symmetric matrix is A + AT = 0.</p>

25 <p>Symmetric matrices have real<a>eigenvalues</a>.</p>

26 Skew-symmetric matrices have purely imaginary or zero eigenvalues.<h3>Explore Our Programs</h3>

27 - <p>No Courses Available</p>

28 <h2>What are the Properties of Symmetric Matrices?</h2>

27 <h2>What are the Properties of Symmetric Matrices?</h2>

29 <p>Some properties that help identify symmetric matrices are listed below:</p>

28 <p>Some properties that help identify symmetric matrices are listed below:</p>

30 <ol><li>The sum of two symmetric matrices is also symmetric. </li>

29 <ol><li>The sum of two symmetric matrices is also symmetric. </li>

31 <li>Eigenvalues of a real symmetric matrix are real. </li>

30 <li>Eigenvalues of a real symmetric matrix are real. </li>

32 <li>Every diagonal matrix is symmetric. </li>

31 <li>Every diagonal matrix is symmetric. </li>

33 <li>The<a>product</a>of two symmetric matrices may or may not be symmetric. </li>

32 <li>The<a>product</a>of two symmetric matrices may or may not be symmetric. </li>

34 <li>The transpose of a symmetric matrix is always equal to the original matrix (AT = A). </li>

33 <li>The transpose of a symmetric matrix is always equal to the original matrix (AT = A). </li>

35 <li>They can be diagonalized using orthogonal matrices, meaning there exists an<a>orthogonal matrix</a>P such that PTAP = D, where D is a diagonal matrix.</li>

34 <li>They can be diagonalized using orthogonal matrices, meaning there exists an<a>orthogonal matrix</a>P such that PTAP = D, where D is a diagonal matrix.</li>

36 </ol><h2>Symmetric Matrices Theorems</h2>

35 </ol><h2>Symmetric Matrices Theorems</h2>

37 <p>Let us understand the two important theorems and their proofs for symmetric matrices.</p>

36 <p>Let us understand the two important theorems and their proofs for symmetric matrices.</p>

38 <p><strong>Theorem 1: </strong>For any square matrix B with real number entries: B + BT is a symmetric matrix, and B - BT is a skew-symmetric matrix. </p>

37 <p><strong>Theorem 1: </strong>For any square matrix B with real number entries: B + BT is a symmetric matrix, and B - BT is a skew-symmetric matrix. </p>

39 <p><strong>Proof: </strong>Let us take A = B + BT</p>

38 <p><strong>Proof: </strong>Let us take A = B + BT</p>

40 <p>Taking the transpose of A,</p>

39 <p>Taking the transpose of A,</p>

41 <p>\(A^T = (B + B^T)^T = B^T + (B^T)^T = B^T + B = B + B^T = A\)</p>

40 <p>\(A^T = (B + B^T)^T = B^T + (B^T)^T = B^T + B = B + B^T = A\)</p>

42 <p>Since \(A^T = T\), this confirms that \(B + B^T\) is symmetric.</p>

41 <p>Since \(A^T = T\), this confirms that \(B + B^T\) is symmetric.</p>

43 <p>Now, let’s take \(C = B - B^T\)</p>

42 <p>Now, let’s take \(C = B - B^T\)</p>

44 <p>Taking the transpose of C,</p>

43 <p>Taking the transpose of C,</p>

45 <p>\(C^T = (B - B^T)^T = B^T - (B^T)^T = B^T - B = - (B - B^T) = - C\)</p>

44 <p>\(C^T = (B - B^T)^T = B^T - (B^T)^T = B^T - B = - (B - B^T) = - C\)</p>

46 <p>Since \(C^T = - C\), this proves that \(B - B^T\) is skew-symmetric.</p>

45 <p>Since \(C^T = - C\), this proves that \(B - B^T\) is skew-symmetric.</p>

47 <p>Let us take an example:</p>

46 <p>Let us take an example:</p>

48 <p><strong>Step 1:</strong>Compute its transpose</p>

47 <p><strong>Step 1:</strong>Compute its transpose</p>

49 <p><strong>Step 2:</strong>Compute B + BT</p>

48 <p><strong>Step 2:</strong>Compute B + BT</p>

50 <p>The matrix is symmetric because \((B + B^T)^T = B + B^T\)</p>

49 <p>The matrix is symmetric because \((B + B^T)^T = B + B^T\)</p>

51 <p><strong>Step 3:</strong>Compute B - BT</p>

50 <p><strong>Step 3:</strong>Compute B - BT</p>

52 <p>This matrix is skew-symmetric because</p>

51 <p>This matrix is skew-symmetric because</p>

53 <p>\((B - B^T)^T = - (B - B^T)\)</p>

52 <p>\((B - B^T)^T = - (B - B^T)\)</p>

54 <p><strong>Theorem 2:</strong> Any square matrix can be written as the sum of a symmetric matrix and a skew-symmetric matrix.</p>

53 <p><strong>Theorem 2:</strong> Any square matrix can be written as the sum of a symmetric matrix and a skew-symmetric matrix.</p>

55 <p><strong>Proof: </strong>Let B be a square matrix.</p>

54 <p><strong>Proof: </strong>Let B be a square matrix.</p>

56 <p>We use the following identity: \(B = \frac{1}{2}(B + B^T) + \frac{1}{2}(B-B^T)\)</p>

55 <p>We use the following identity: \(B = \frac{1}{2}(B + B^T) + \frac{1}{2}(B-B^T)\)</p>

57 <p>Where, BT is the transpose of matrix B.</p>

56 <p>Where, BT is the transpose of matrix B.</p>

58 <p>\(\frac{1}{2}(B +BT)\) is symmetric because:</p>

57 <p>\(\frac{1}{2}(B +BT)\) is symmetric because:</p>

59 <p>\(\frac{1}{2}(B+B^T)T = \frac{1}{2}(B^T+(B^T)^T) = \frac{1}{2}(B^T+B) = \frac{1}{2}(B + B^T)\)</p>

58 <p>\(\frac{1}{2}(B+B^T)T = \frac{1}{2}(B^T+(B^T)^T) = \frac{1}{2}(B^T+B) = \frac{1}{2}(B + B^T)\)</p>

60 <p>\(\frac{1}{2}(B -B^T)\) is skew-symmetric because: \(\frac{1}{2}(B-B^T)^T=\)\(\frac{1}{2}(B^T-B) = -\frac{1}{2}(B - B^T )\).</p>

59 <p>\(\frac{1}{2}(B -B^T)\) is skew-symmetric because: \(\frac{1}{2}(B-B^T)^T=\)\(\frac{1}{2}(B^T-B) = -\frac{1}{2}(B - B^T )\).</p>

61 <p>Hence, the square matrix B can be expressed as the sum of a symmetric and skew-symmetric matrix.</p>

60 <p>Hence, the square matrix B can be expressed as the sum of a symmetric and skew-symmetric matrix.</p>

62 <p>Let us use the same matrix from the previous example:</p>

61 <p>Let us use the same matrix from the previous example:</p>

63 <p><strong>Step 1:</strong>Calculate the symmetric part:</p>

62 <p><strong>Step 1:</strong>Calculate the symmetric part:</p>

64 <p><strong>Step 2:</strong>Calculate the skew-symmetric part:</p>

63 <p><strong>Step 2:</strong>Calculate the skew-symmetric part:</p>

65 <p><strong>Step 3: </strong> Verify their sum</p>

64 <p><strong>Step 3: </strong> Verify their sum</p>

66 <h2>Tips and Tricks to Master Symmetric Matrix</h2>

65 <h2>Tips and Tricks to Master Symmetric Matrix</h2>

67 <p>Symmetric matrices are important in<a>linear algebra</a>and here are some tips and tricks for students to master this concept easily. </p>

66 <p>Symmetric matrices are important in<a>linear algebra</a>and here are some tips and tricks for students to master this concept easily. </p>

68 <ul><li>Check symmetry visually first: Look for a mirror-like pattern across the main diagonal. If the element in row 𝑖, column 𝑗 is equal to the element in row 𝑗, column 𝑖, it’s symmetric.</li>

67 <ul><li>Check symmetry visually first: Look for a mirror-like pattern across the main diagonal. If the element in row 𝑖, column 𝑗 is equal to the element in row 𝑗, column 𝑖, it’s symmetric.</li>

69 <li>Use transpose as a quick test: Remember: 𝐴=𝐴𝑇. Simply swap rows and columns and check equality.</li>

68 <li>Use transpose as a quick test: Remember: 𝐴=𝐴𝑇. Simply swap rows and columns and check equality.</li>

70 <li>Focus on the diagonal elements: Diagonal elements remain unchanged. They can help you quickly verify symmetry without checking all elements.</li>

69 <li>Focus on the diagonal elements: Diagonal elements remain unchanged. They can help you quickly verify symmetry without checking all elements.</li>

71 <li>Understand eigenvalue properties: Symmetric matrices always have real eigenvalues. Knowing this helps in solving problems faster, especially in PCA or physics applications.</li>

70 <li>Understand eigenvalue properties: Symmetric matrices always have real eigenvalues. Knowing this helps in solving problems faster, especially in PCA or physics applications.</li>

72 <li>Use symmetry to simplify calculations: For example, in<a>solving linear equations</a>or finding<a>determinants</a>, leverage the symmetry to reduce computation. Only the upper or lower triangle of the matrix may need examination.</li>

71 <li>Use symmetry to simplify calculations: For example, in<a>solving linear equations</a>or finding<a>determinants</a>, leverage the symmetry to reduce computation. Only the upper or lower triangle of the matrix may need examination.</li>

73 </ul><h2>Common Mistakes and How to Avoid Them in Symmetric Matrix</h2>

72 </ul><h2>Common Mistakes and How to Avoid Them in Symmetric Matrix</h2>

74 <p>While working with symmetric matrices, students often make subtle, avoidable errors. This section of the article highlights those common mistakes for students in order to identify and avoid them.</p>

73 <p>While working with symmetric matrices, students often make subtle, avoidable errors. This section of the article highlights those common mistakes for students in order to identify and avoid them.</p>

75 <h2>Real-life Applications of Symmetric Matrix</h2>

74 <h2>Real-life Applications of Symmetric Matrix</h2>

76 <p>From analyzing mechanical stress in bridges to simplifying<a>data</a>in machine learning, symmetric matrices help model, optimize, and solve real-life problems efficiently. Some real-life applications of symmetric matrices are listed below:</p>

75 <p>From analyzing mechanical stress in bridges to simplifying<a>data</a>in machine learning, symmetric matrices help model, optimize, and solve real-life problems efficiently. Some real-life applications of symmetric matrices are listed below:</p>

77 <ul><li><strong>Representing stiffness matrix in structural engineering: </strong>In civil and mechanical engineering, symmetric matrices represent the stiffness matrices in finite element methodology. These matrices help simulate how structures like bridges or buildings may deform under force. </li>

76 <ul><li><strong>Representing stiffness matrix in structural engineering: </strong>In civil and mechanical engineering, symmetric matrices represent the stiffness matrices in finite element methodology. These matrices help simulate how structures like bridges or buildings may deform under force. </li>

78 </ul><ul><li><strong>Scaling, shearing, and reflective transformations in computer graphics: </strong>Symmetric matrices help define how objects appear on-screen when they are being moved, rotated, or mirrored. </li>

77 </ul><ul><li><strong>Scaling, shearing, and reflective transformations in computer graphics: </strong>Symmetric matrices help define how objects appear on-screen when they are being moved, rotated, or mirrored. </li>

79 </ul><ul><li><strong>Intermediate calculations in Google PageRank algorithm: </strong>The Google PageRank matrix isn't symmetric itself but requires intermediate calculations involving symmetric matrices. They simplify eigenvalue problems or balance link weights. </li>

78 </ul><ul><li><strong>Intermediate calculations in Google PageRank algorithm: </strong>The Google PageRank matrix isn't symmetric itself but requires intermediate calculations involving symmetric matrices. They simplify eigenvalue problems or balance link weights. </li>

80 </ul><ul><li><strong>Blurring and filtering in image processing: </strong>In digital image processing, symmetric matrices are used for tasks like blurring, edge detection and noise reduction. Symmetry in kernel filters ensures uniform behavior in all directions. </li>

79 </ul><ul><li><strong>Blurring and filtering in image processing: </strong>In digital image processing, symmetric matrices are used for tasks like blurring, edge detection and noise reduction. Symmetry in kernel filters ensures uniform behavior in all directions. </li>

81 </ul><ul><li><strong>Network analysis: </strong>In graph theory, for example social networks, transportation systems, or communication systems, adjacency matrices of undirected graphs are symmetric.</li>

80 </ul><ul><li><strong>Network analysis: </strong>In graph theory, for example social networks, transportation systems, or communication systems, adjacency matrices of undirected graphs are symmetric.</li>

82 </ul><h3>Problem 1</h3>

81 </ul><h3>Problem 1</h3>

83 <p>Is the given matrix symmetric?</p>

82 <p>Is the given matrix symmetric?</p>

84 <p>Okay, lets begin</p>

83 <p>Okay, lets begin</p>

85 <p>Yes. </p>

84 <p>Yes. </p>

86 <h3>Explanation</h3>

85 <h3>Explanation</h3>

87 <p>Since a12 = a21 = 2, the matrix is symmetric.</p>

86 <p>Since a12 = a21 = 2, the matrix is symmetric.</p>

88 <p>Well explained 👍</p>

87 <p>Well explained 👍</p>

89 <h3>Problem 2</h3>

88 <h3>Problem 2</h3>

90 <p>Let Find a symmetric matrix using the formula 1/2(B+B to the power T).</p>

89 <p>Let Find a symmetric matrix using the formula 1/2(B+B to the power T).</p>

91 <p>Okay, lets begin</p>

90 <p>Okay, lets begin</p>

92 <p>\(\begin{bmatrix} 1 & 3.5 \\ 3.5 & 2 \end{bmatrix} \)</p>

91 <p>\(\begin{bmatrix} 1 & 3.5 \\ 3.5 & 2 \end{bmatrix} \)</p>

93 <h3>Explanation</h3>

92 <h3>Explanation</h3>

94 <p>First, find the transpose BT: </p>

93 <p>First, find the transpose BT: </p>

95 <p>\( B^{T} = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix} \) </p>

94 <p>\( B^{T} = \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix} \) </p>

96 <p>Using formula, we get: </p>

95 <p>Using formula, we get: </p>

97 <p>\(\frac{1}{2}(B + B^{T}) = \frac{1}{2} \left( \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix} + \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix} \right) = \frac{1}{2} \begin{bmatrix} 2 & 7 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 1 & 3.5 \\ 3.5 & 2 \end{bmatrix} \)</p>

96 <p>\(\frac{1}{2}(B + B^{T}) = \frac{1}{2} \left( \begin{bmatrix} 1 & 3 \\ 4 & 2 \end{bmatrix} + \begin{bmatrix} 1 & 4 \\ 3 & 2 \end{bmatrix} \right) = \frac{1}{2} \begin{bmatrix} 2 & 7 \\ 7 & 4 \end{bmatrix} = \begin{bmatrix} 1 & 3.5 \\ 3.5 & 2 \end{bmatrix} \)</p>

98 <p>Well explained 👍</p>

97 <p>Well explained 👍</p>

99 <h3>Problem 3</h3>

98 <h3>Problem 3</h3>

100 <p>The given matrix is symmetric. Find the value of x</p>

99 <p>The given matrix is symmetric. Find the value of x</p>

101 <p>Okay, lets begin</p>

100 <p>Okay, lets begin</p>

102 <p> x = 5 </p>

101 <p> x = 5 </p>

103 <h3>Explanation</h3>

102 <h3>Explanation</h3>

104 <p>For a symmetric matrix, a12 = a21 So x = 5. </p>

103 <p>For a symmetric matrix, a12 = a21 So x = 5. </p>

105 <p>Well explained 👍</p>

104 <p>Well explained 👍</p>

106 <h3>Problem 4</h3>

105 <h3>Problem 4</h3>

107 <p>Check if this 3 × 3 matrix is symmetric.</p>

106 <p>Check if this 3 × 3 matrix is symmetric.</p>

108 <p>Okay, lets begin</p>

107 <p>Okay, lets begin</p>

109 <p> Yes, the matrix is symmetric. </p>

108 <p> Yes, the matrix is symmetric. </p>

110 <h3>Explanation</h3>

109 <h3>Explanation</h3>

111 <p>The transpose and the matrix are equal. </p>

110 <p>The transpose and the matrix are equal. </p>

112 <p>\(D^{T} = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{bmatrix} = D \) </p>

111 <p>\(D^{T} = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 4 & 5 \\ 3 & 5 & 6 \end{bmatrix} = D \) </p>

113 <p>Well explained 👍</p>

112 <p>Well explained 👍</p>

114 <h3>Problem 5</h3>

113 <h3>Problem 5</h3>

115 <p>Is the given diagonal matrix symmetric?</p>

114 <p>Is the given diagonal matrix symmetric?</p>

116 <p>Okay, lets begin</p>

115 <p>Okay, lets begin</p>

117 <p> Yes, all square diagonal matrices are symmetric.</p>

116 <p> Yes, all square diagonal matrices are symmetric.</p>

118 <h3>Explanation</h3>

117 <h3>Explanation</h3>

119 <p>Transpose of a diagonal matrix is the same as the original: ET = E </p>

118 <p>Transpose of a diagonal matrix is the same as the original: ET = E </p>

120 <p>Well explained 👍</p>

119 <p>Well explained 👍</p>

121 <h2>FAQs on Symmetric Matrix</h2>

120 <h2>FAQs on Symmetric Matrix</h2>

122 <h3>1. How do you know if a matrix is a symmetric matrix?</h3>

121 <h3>1. How do you know if a matrix is a symmetric matrix?</h3>

123 <p> A matrix is symmetric if it is equal to its transpose. That is, for a square matrix A, if A = AT then the matrix is symmetric. </p>

122 <p> A matrix is symmetric if it is equal to its transpose. That is, for a square matrix A, if A = AT then the matrix is symmetric. </p>

124 <h3>2.What is the sum of two symmetric matrices?</h3>

123 <h3>2.What is the sum of two symmetric matrices?</h3>

125 <p>The sum of two symmetric matrices is also a symmetric matrix only if both matrices are of the same order. Mathematically, if A = AT and B = BT, then (A + B)T= AT+BT= A + B = A + B, which is symmetric. </p>

124 <p>The sum of two symmetric matrices is also a symmetric matrix only if both matrices are of the same order. Mathematically, if A = AT and B = BT, then (A + B)T= AT+BT= A + B = A + B, which is symmetric. </p>

126 <h3>3.What is the sum of symmetric and non-symmetric matrices?</h3>

125 <h3>3.What is the sum of symmetric and non-symmetric matrices?</h3>

127 <p>The sum of a symmetric and a non-symmetric (non-symmetric) matrix is not necessarily symmetric. The resulting matrix must be checked by finding its transpose - if it equals the original matrix, it’s symmetric; otherwise, it’s not </p>

126 <p>The sum of a symmetric and a non-symmetric (non-symmetric) matrix is not necessarily symmetric. The resulting matrix must be checked by finding its transpose - if it equals the original matrix, it’s symmetric; otherwise, it’s not </p>

128 <h3>4.Do all symmetric matrices have zeroes on the diagonal?</h3>

127 <h3>4.Do all symmetric matrices have zeroes on the diagonal?</h3>

129 <p> No, symmetric matrices can have any value on the diagonal. </p>

128 <p> No, symmetric matrices can have any value on the diagonal. </p>

130 <h3>5.Are all symmetric matrices invertible?</h3>

129 <h3>5.Are all symmetric matrices invertible?</h3>

131 <p>No, not all symmetric matrices are invertible. A matrix is only invertible when its determinant is non-zero. </p>

130 <p>No, not all symmetric matrices are invertible. A matrix is only invertible when its determinant is non-zero. </p>

132 <h3>6.Why is it important for my child to learn symmetric matrices?</h3>

131 <h3>6.Why is it important for my child to learn symmetric matrices?</h3>

133 <p>Symmetric matrices are foundational in<a>math</a>and science. They are used in physics (vibrations), engineering (stability analysis), and AI (data patterns), helping students develop logical and problem-solving skills.</p>

132 <p>Symmetric matrices are foundational in<a>math</a>and science. They are used in physics (vibrations), engineering (stability analysis), and AI (data patterns), helping students develop logical and problem-solving skills.</p>

134 <h3>7.Are symmetric matrices difficult for students to understand?</h3>

133 <h3>7.Are symmetric matrices difficult for students to understand?</h3>

135 <p>Not if approached step by step. Recognizing mirror patterns, practicing small matrices, and using visual aids can make it much easier.</p>

134 <p>Not if approached step by step. Recognizing mirror patterns, practicing small matrices, and using visual aids can make it much easier.</p>

136 <h3>8.How can parents support their children in mastering the topic of Symmetric Matrix?</h3>

135 <h3>8.How can parents support their children in mastering the topic of Symmetric Matrix?</h3>

137 <p>Encourage practice with small examples, use visual tools (like grids or diagrams), and relate concepts to real-life applications such as AI, robotics, or engineering problems.</p>

136 <p>Encourage practice with small examples, use visual tools (like grids or diagrams), and relate concepts to real-life applications such as AI, robotics, or engineering problems.</p>

138 <h2>Jaskaran Singh Saluja</h2>

137 <h2>Jaskaran Singh Saluja</h2>

139 <h3>About the Author</h3>

138 <h3>About the Author</h3>

140 <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>

139 <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>

141 <h3>Fun Fact</h3>

140 <h3>Fun Fact</h3>

142 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>

141 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>