(B) Let $S = A + A^T$. To check if $S$ is symmetric,we find its transpose: $S^T = (A + A^T)^T$. Using the property of transpose $(X + Y)^T = X^T + Y^T

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(B) Let $S = A + A^T$. To check if $S$ is symmetric,we find its transpose: $S^T = (A + A^T)^T$. Using the property of transpose $(X + Y)^T = X^T + Y^T$,we get: $S^T = A^T + (A^T)^T$. Since $(A^T)^T = A$,we have: $S^T = A^T + A = A + A^T = S$. Since $S^T = S$,the matrix $A + A^T$ is a symmetric matrix.

Class 12 Mathematics 3 and 4 .Determinants and Matrices Special types of matrices, Transpose of matrices and Trace of matrices

Easy

If $A$ is a square matrix,then $A + A^T$ is:

A
Non-singular matrix
B
Symmetric matrix
C
Skew-symmetric matrix
D
Unit matrix

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Class 12

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Chapter

3 and 4 .Determinants and Matrices

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Special types of matrices, Transpose of matrices and Trace of matrices

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MediumKCET 2018

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If $A$ is a square matrix,then $A + A^T$ is:

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Express the matrix $A = \left[\begin{array}{cc}1 & 5 \\ -1 & 2\end{array}\right]$ as the sum of a symmetric and a skew-symmetric matrix.

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