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  • For the matrix A = [1 5 6 7], verify that (i) (A + A') is a symmetric matrix

Q8.    For the matrix A = \begin{bmatrix} 1 & 5\\ 6 & 7 \end{bmatrix}, verify that

            (i) (A + A') is a symmetric matrix.

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A = \begin{bmatrix} 1 & 5\\ 6 & 7 \end{bmatrix}

A' = \begin{bmatrix} 1 & 6\\ 5 & 7 \end{bmatrix}

A + A'= \begin{bmatrix} 1 & 5\\ 6 & 7 \end{bmatrix}  + \begin{bmatrix} 1 & 6\\ 5 & 7 \end{bmatrix}

A + A'= \begin{bmatrix} 1+1 & 5+6\\ 6+5 & 7+7 \end{bmatrix}

A + A'= \begin{bmatrix}2 & 11\\ 11& 14 \end{bmatrix}

(A + A')'= \begin{bmatrix}2 & 11\\ 11& 14 \end{bmatrix}

We have A+A'=(A + A')'

Hence ,  (A + A') is a symmetric matrix.

Posted by

seema garhwal

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