Question

If $\left[\begin{array}{cc}x+y& a+b\\ a-b& s-y\end{array}\right]=\left[\begin{array}{cc}5& -1\\ 3& -5\end{array}\right]$, then the values of $x,y,a,b$ are respectively.

• A. $0,-5,1,2$
• B. $0,5,1,-2$
• C. $0,5,-1,2$
• D. $0,-5,1,-2$

Answer 1

The correct option is B $0,5,1,-2$

$\left[\begin{array}{cc}x+y& a+b\\ a-b& x-y\end{array}\right]=\left[\begin{array}{cc}5& -1\\ 3& -5\end{array}\right]$

$\Rightarrow x+y=5⟶\left(1\right)$

$\Rightarrow a+b=-1⟶\left(2\right)$

$\Rightarrow a-b=3⟶\left(3\right)$

$\Rightarrow x-y=-5⟶\left(4\right)$

Adding equations $\left(1\right)\&\left(4\right),$ we get

$\Rightarrow 2x=0$

$x=0$

Put $x=0$ in equation $\left(1\right),$ we get

$\Rightarrow y=5$

Now, adding equations $\left(2\right),$ we get

$\Rightarrow 1+b=-1$

$b=-2$

$\therefore x=0,y=5,a=1,b=-2$

Hence, the answer is $0,5,1,-2.$