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 a, b, c, x, y 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 $c=-1$
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