Question

If $\left[\begin{array}{ccc}x+3& z+4& 2y-7\\ -6& a-1& 0\\ b-3& -21& 0\end{array}\right]=\left[\begin{array}{ccc}0& 6& 3y-2\\ -6& -3& 2c+2\\ 2b+4& -21& 0\end{array}\right]$
Find the values of $a,b,c,x,y\text{and}z$.

Answer 1

Given:$\left[\begin{array}{ccc}x+3& z+4& 2y-7\\ -6& a-1& 0\\ b-3& -21& 0\end{array}\right]=\left[\begin{array}{ccc}0& 6& 3y-2\\ -6& -3& 2c+2\\ 2b+4& -21& 0\end{array}\right]$
Comparing corresponding elements,
$x+3=0\Rightarrow x=0-3$
$\Rightarrow x=-3$
$2y-7=3y-2\Rightarrow 2y-3y=-2+7$
$\Rightarrow y=-5$
$z+4=6\Rightarrow z=6-4$
$\Rightarrow z=2$
$a-1=-3\Rightarrow a=-3+1$
$\Rightarrow a=-2$
$b-3=2b+4\Rightarrow b-2b=4+3$
$\Rightarrow b=-7$
$2c+2=0$
$\Rightarrow c=-1$
$\therefore a=-2,b=-7,c=-1,x=-3,y=-5$ and $z=2.$