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