Question

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

Answer 1

$a=1,b=2,c=3,d=4$

We have,

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

Solving $2a+b=4$ and $a-2b=-3$ simultaneously, we get $a=1$ and $b=2$.

Solving $5c-d=11$ and $4c+3d=24$ simultaneously, we get $c=3$ and $d=4$.