Question

Find $a,b,c,d$ if $\left[\begin{array}{cc}d+1& 10+a\\ 3b-2& a-4\end{array}\right]=\left[\begin{array}{cc}2& 2a+1\\ b-5& 4c\end{array}\right]$

Answer 1

Equating the corresponding elements of the two matrices, we have

$d+1=2\Rightarrow d=2-1=1$

$10+a=2a+1$

$\Rightarrow 2a-a=10-1$

$\therefore a=9$

$3b-2=b-5\Rightarrow 3b-b=-5+2$

$\Rightarrow 2b=-3$

$\Rightarrow 2b=-3$

$\therefore b=\frac{-3}{2}$

$a-4=4c$

$\Rightarrow 4c=a-4=9-4=5$

$\therefore c=\frac{5}{4}$

$\therefore a=9,b=\frac{-3}{2},c=\frac{5}{4},d=1$