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(A) Given the matrix equation:$2\begin{bmatrix} 1 & 3 \ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \

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$ x=3, y=3 $

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(A) Given the matrix equation:$2\begin{bmatrix} 1 & 3 \ 0 & x \end{bmatrix} + \begin{bmatrix} y & 0 \ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \ 1 & 8 \end{bmatrix}$Multiplying the first matrix by $2$,we get:$\begin{bmatrix} 2 & 6 \ 0 & 2x \end{bmatrix} + \begin{bmatrix} y & 0 \ 1 & 2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \ 1 & 8 \end{bmatrix}$Adding the two matrices on the left side:$\begin{bmatrix} 2+y & 6+0 \ 0+1 & 2x+2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \ 1 & 8 \end{bmatrix}$$\begin{bmatrix} 2+y & 6 \ 1 & 2x+2 \end{bmatrix} = \begin{bmatrix} 5 & 6 \ 1 & 8 \end{bmatrix}$By comparing the corresponding elements of the two matrices:$2+y = 5 \Rightarrow y = 5-2 = 3$$2x+2 = 8 \Rightarrow 2x = 6 \Rightarrow x = 3$Thus,the values are $x=3$ and $y=3$.

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 values of $ x $ and $ y $ are:

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