Question

If $\left(\begin{array}{cc}1& 2\\ 2& 1\end{array}\right)\left(\begin{array}{c}x\\ y\end{array}\right)=\left(\begin{array}{c}2\\ 4\end{array}\right)$, then the value of $x$ and $y$ respectively are

• A. $2,0$
• B. $0,2$
• C. $0,-2$
• D. $1,1$

Answer 1

The correct option is A $2,0$

$\left(\begin{array}{cc}1& 2\\ 2& 1\end{array}\right)$$\left(\begin{array}{c}x\\ y\end{array}\right)$= $\left(\begin{array}{c}2\\ 4\end{array}\right)$

$⟹\left(\begin{array}{c}x+2y\\ 2x+y\end{array}\right)$ = $\left(\begin{array}{c}2\\ 4\end{array}\right)$

$x+2y=2$............(i)

$2x+y=4$.............(ii)

By solving (i) & (ii) we get, $x=2,y=0$

Option A is correct.