Question

If $\left[\begin{array}{cc}-2& 5\\ 3& -1\end{array}\right]\left[\begin{array}{c}x\\ y\end{array}\right]=\left[\begin{array}{cc}1& 2\\ 3& 4\end{array}\right]\left[\begin{array}{c}3\\ -1\end{array}\right]$ then $(x,y)$ is

• A. (1, 2)
• B. (-1, 2)
• C. (1, - 2)
• D. (2, 1)

Answer 1

Answer: (D)

$\left|\begin{array}{cc}-2& 5\\ 3& -1\end{array}\right|\left|\begin{array}{c}x\\ y\end{array}\right|=\left|\begin{array}{cc}1& 2\\ 3& 4\end{array}\right|\left|\begin{array}{c}3\\ -1\end{array}\right|$
$\Rightarrow \left|\begin{array}{c}-2x+5y\\ 3x-y\end{array}\right|=\left|\begin{array}{c}1\\ 5\end{array}\right|$
$\Rightarrow -2x+5y=1,3x-y=5$
or $y=3x-5$
$\Rightarrow -2x+5(3x-5)=1$
$\Rightarrow -2x+15x-25=1$
$\Rightarrow 13x=26\Rightarrow x=2$
Substituting $x=2$ in (i), we get
$y=6-5=1$
Hence, $(x,y)=(2,1)$