Question

Find the value of $b$ if
$\left[\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right]=\left[\begin{array}{cc}-1& 5\\ 0& 13\end{array}\right]$

Answer 1

Since $\left(\begin{array}{cc}a-b& 2a+c\\ 2a-b& 3c+d\end{array}\right)=\left(\begin{array}{cc}-1& 5\\ 0& 13\end{array}\right)$

Equating the matrices we get,

$a-b=-1................\left(1\right)$

$2a+c=5................\left(2\right)$

$2a-b=0................\left(3\right)$

$3c+d=13................\left(4\right)$

Now from equation (3) we get $b=2a$

Substituting $b=2a$ in equation (1) we get,

$a-2a=-1⟹-a=-1⟹a=1$

Hence, $a=1$.,$b=2$