Question

Find x and y, if 2$\begin{bmatrix}1&3\\\0&x\end{bmatrix}$+$\begin{bmatrix}y&0\\\1&2\end{bmatrix}$=$\begin{bmatrix}5&6\\\1&8\end{bmatrix}$

Answer 1

2$\begin{bmatrix}1&3\\\0&x\end{bmatrix}$+$\begin{bmatrix}y&0\\\1&2\end{bmatrix}$=$\begin{bmatrix}5&6\\\1&8\end{bmatrix}$

$\Rightarrow$ $\begin{bmatrix}2&6\\\0&2x\end{bmatrix}$ +$\begin{bmatrix}y&0\\\1&2\end{bmatrix}$=$\begin{bmatrix}5&6\\\1&8\end{bmatrix}$

$\Rightarrow \begin{bmatrix}2+y&6\\\1&2x+2\end{bmatrix}$=$\begin{bmatrix}5&6\\\1&8\end{bmatrix}$
Comparing the corresponding elements of these two matrices, we have:
2+y=5
$\Rightarrow$ y=3.
2x+2=8
$\Rightarrow$ x=3
∴x = 3 and y = 3