If $A=\left[\begin{array}{ll}x & 3 \\ 2 & y\end{array}\right], B=\left[\begin{array}{cc}2 y & 1 \\ 3 & x\end{array}\right]$ and $A+2 B=\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]$ then the value of (x, y) is:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) - $(-2,2)$
$A+2 B=\left[\begin{array}{cc}x+4y & 5 \\ 8 & y+2x\end{array}\right]\left[\begin{array}{cc}6 & 5 \\ 8 & -2\end{array}\right]$
$x+4y=6$ ...(1)
$y+2x=-2$ ...(2)
eq. (1) × 2 - eq. (2)
$2x+8y-y-2x=12-2$
$7y=14⇒y=2$
from (1) $x=-2$
$(-2,2)$