Obtain the values of a, b, c, x, y and z.
Question:

If $\left[\begin{array}{rcc}x+3 & z+4 & 2 y-7 \\ 4 x+6 & a-1 & 0 \\ b-3 & 3 b & z+2 c\end{array}\right]=\left[\begin{array}{rrr}0 & 6 & 3 y-2 \\ 2 x & -3 & 2 c-2 \\ 2 b+4 & -21 & 0\end{array}\right]$

Obtain the values of abcxy and z.

Solution:

Since all the corresponding element of a matrix are equal,

$x+3=0$

$\Rightarrow x=-3$

Also,

$2 y-7=3 y-2$

$\Rightarrow 2 y-3 y=-2+7$

$\Rightarrow-y=5$

$\Rightarrow y=-5$

$z+4=6$

$\Rightarrow z=6-4$

$\Rightarrow z=2$

$a-1=-3$

$\Rightarrow a=-3+1$

$\Rightarrow a=-2$

$3 b=-21$

$\Rightarrow b=-7$

$z+2 c=0$

$\Rightarrow 2=-2 c$

$\Rightarrow c=-1$

Thus,

$x=-3, y=-5, z=2, a=-2, b=-7$ and $c=-1$