Question

If $\left[\begin{array}{cc}x& 0\\ 1& y\end{array}\right]-\left[\begin{array}{cc}2& -4\\ -3& -4\end{array}\right]=\left[\begin{array}{cc}3& 5\\ 6& 3\end{array}\right]-\left[\begin{array}{cc}2& 1\\ 2& 1\end{array}\right],$ then $x=$ ___ and $y=$___.

• A. $3,5$
• B. $3,-2$
• C. $-3,-3$
• D. $-3,2$

Answer 1

The correct option is B $3,-2$

Given,

$\left[\begin{array}{cc}x& 0\\ 1& y\end{array}\right]-\left[\begin{array}{cc}2& -4\\ -3& -4\end{array}\right]=\left[\begin{array}{cc}3& 5\\ 6& 3\end{array}\right]-\left[\begin{array}{cc}2& 1\\ 2& 1\end{array}\right]$

$\Rightarrow \left[\begin{array}{cc}x-2& 4\\ 4& y+4\end{array}\right]=\left[\begin{array}{cc}1& 4\\ 4& 2\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}x-2=1\\ y+4=2\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}x=1+2\\ y=2-4\end{array}\right]$

$\Rightarrow \left[\begin{array}{c}x=3\\ y=-2\end{array}\right]$