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If A = \( \begin{bmatrix} 4& 1 \\[0.3em] 5& 8\\[0.3em] \end{bmatrix}\), show that (A + A’) is symmetric.

A = [(4,1)(5,8)]

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Given A = \( \begin{bmatrix} 4 &1 \\[0.3em] 5 & 8 \\[0.3em] \end{bmatrix}\).

To Prove: A + A’ is symmetric.(Note:A matrix P is symmetric if P’ = P)

Proof: We will find A’,

A' = \( \begin{bmatrix} 4 &1 \\[0.3em] 5 & 8 \\[0.3em] \end{bmatrix}\)

Now let us take P = A + A’

\(\Rightarrow P'=P\)

Hence A + A’ is a symmetric matrix.

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