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  4. If 2[1&3 0&x]+[y&0 1&2]=[5&6 1&8], then the value of x and y are

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Q. If $2\begin{bmatrix}1&3\\ 0&x\end{bmatrix}+\begin{bmatrix}y&0\\ 1&2\end{bmatrix}=\begin{bmatrix}5&6\\ 1&8\end{bmatrix}$, then the value of $x$ and $y$ are

KCETKCET 2017Matrices

Solution:

We have,
$2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix}+\begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix}=\begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}$
$\Rightarrow \begin{bmatrix}2+y & 6 \\ 1 & 2 x+2\end{bmatrix}=\begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}$
$ \therefore \, 2+y=5$ and $ 2 x+2=8 $
$ \Rightarrow y=3$ and $x=3 $
$ \therefore x=3, y=3$