If A= 1&2 3&4 , find A+A^T. - Vidyadip

Question

If $\text{A}=\begin{bmatrix}1&2\\3&4 \end{bmatrix}$, find $A+A^T.$

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Answer

Given: $\text{A}=\begin{bmatrix}1&2\\3&4 \end{bmatrix}$
$\text{A}^{\text{T}}=\begin{bmatrix}1&3\\2&4 \end{bmatrix}$
$\text{A+A}^{\text{T}}=\begin{bmatrix}1&2\\3&4 \end{bmatrix}+\begin{bmatrix}1&3\\2&4 \end{bmatrix}$
$\Rightarrow\text{A+A}^{\text{T}}=\begin{bmatrix}1+1&2+3\\3+2&4+4 \end{bmatrix}$
$\Rightarrow\text{A+A}^{\text{T}}=\begin{bmatrix}2&5\\5&8 \end{bmatrix}$

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