# If A = [(4,1)(5,8)] , show that (A + A’) is symmetric.

38 views
in Matrices
closed

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)]

+1 vote
by (31.5k points)
selected by

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.