Question
Find matrix $\text{A},\text{if}\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}+\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}$
✓
Answer
Given,
$\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}+\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}$
$\Rightarrow\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}-\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}$
$\Rightarrow\text{A}=\begin{bmatrix}9-1&-1-2&4+1\\-2-0&1-4&3-9\end{bmatrix}$
Hence,
$\text{A}=\begin{bmatrix}8&-3&5\\-2&-3&-6\end{bmatrix}$
$\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}+\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}$
$\Rightarrow\text{A}=\begin{bmatrix}9&-1&4\\-2&1&3\end{bmatrix}-\begin{bmatrix}1&2&-1\\0&4&9\end{bmatrix}$
$\Rightarrow\text{A}=\begin{bmatrix}9-1&-1-2&4+1\\-2-0&1-4&3-9\end{bmatrix}$
Hence,
$\text{A}=\begin{bmatrix}8&-3&5\\-2&-3&-6\end{bmatrix}$
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