If \(2\begin{bmatrix}3 & 4\\5 & x\end{bmatrix}+\begin{bmatrix}1 & y\\0 & 1\end{bmatrix}=\begin{bmatrix}7 & 0\\10 & 5\end{bmatrix}\), then the value of x - y is:
Answer & explanation
Correct answer: option 3
\(2\begin{bmatrix}3 & 4\\5 & x\end{bmatrix}=\begin{bmatrix}6 & 8\\10 & 2x\end{bmatrix}\) ...(i)
According to questions,
$\begin{bmatrix}6 & 8\\10 & 2x\end{bmatrix}+\begin{bmatrix}1 & y\\0 & 1\end{bmatrix}=\begin{bmatrix}7 & 0\\10 & 5\end{bmatrix}$ from eq. (i)
$\begin{bmatrix}7 & 8+y\\10 & 2x+1\end{bmatrix}$
⇒ 8 + y = 0
y = 0 - 8
y = -8
and 2x + 1= 5
2x = 5 - 1 = 4
2x = 4
$x = \frac{4}{2}=2⇒x=2$
So, value of x - y = 2 - (-8) = 10