Question

Find the values of $a,b,c,d$
$\left[\begin{array}{cc}2a+b& a-2b\\ 5c-d& 4c+3d\end{array}\right]=\left[\begin{array}{cc}4& -3\\ 11& 24\end{array}\right]$

Answer 1

$\left[\begin{array}{cc}2a+b& a-2b\\ 5c-d& 4c+3d\end{array}\right]=\left[\begin{array}{cc}4& -3\\ 11& 24\end{array}\right]$

When two matrices are equal then their corresponding elements are equal

i.e., $2a+b=4$ and $a-2b=-3$

By solving, we get

$a=1,b=2$

$5c-d=11$ and $4c+3d=24$

By solving, we get

$c=3,d=4$

$\therefore$ The values of $a,b,c$ and $d$ are $1,2,3$ and $4$ respectively.