Question

Find the values of 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

\[Given: 2\begin{bmatrix}1 & 3 \\ 0 & x\end{bmatrix} + \begin{bmatrix}y & 0 \\ 1 & 2\end{bmatrix} = \begin{bmatrix}5 & 6 \\ 1 & 8\end{bmatrix}\] 

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

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

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

\[ \therefore 2 + y = \text{5 and }2x + 2 = 8\] 

\[ \Rightarrow y =\text{ 5 - 2 and } 2x = 8 - 2\] 

\[ \Rightarrow y = \text{3 and }2x = 6\] 

\[ \Rightarrow x = \frac{6}{2} = 3\]