Question

Find p,q,r and s, if $\left[\begin{array}{cc}p+4& 2q-7\\ s-3& r+2s\end{array}\right]=\left[\begin{array}{cc}6& -3\\ 2& 14\end{array}\right]$

Answer 1

$[\begin{array}{cc}p+4& 2q-7\\ s-3& r+2s\end{array}]=[\begin{array}{cc}6& -3\\ 2& 14\end{array}]$

We know that two matrices are equal if and only if corresponding elements of both matrices are equal

Hence,

$p+4=6$

$\to p=6-4=2\dots \left(1\right)$

and

$2q-7=-3$

$\to 2q=7-3=4$

$\to q=\frac{4}{2}=2\dots .\left(2\right)$

and

$s-3=2$

$\to s=3+2=5\dots \left(3\right)$

and

$r+2s=14$

$\to r+2\times 5=14$

$\to r=14-10=4\dots \left(4\right)$

Hence value of $p=2,q=2,r=4,and5$