For the matrix A= \begin{bmatrix} 2 &3 \\ 5&7 \end{bmatrix},   find  \left ( A+{A}' \right )   and verify that it is a symmetric matrix.

 

 

 

 
 
 
 
 

Answers (1)

A= \begin{bmatrix} 2 &3 \\ 5 &7 \end{bmatrix}\; \; find \left ( A+{A}' \right ) as
A+{A}'= \begin{bmatrix} 2 &3 \\ 5 &7 \end{bmatrix}+\begin{bmatrix} 2 &5 \\ 3 &7 \end{bmatrix}= \begin{bmatrix} 4 &8 \\ 8 &14 \end{bmatrix}
Also \left ( A+{A}' \right )'= \begin{bmatrix} 4 & 8\\ 8&14 \end{bmatrix}= A+{A}',so\: A+{A}'    is a symmetric matrix.

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