Question

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

Answer 1

Since all the corresponding element of a matrix are equal,

$$\begin{gathered} x+3=0 \\ \Rightarrow x=-3 \\ \mathrm{Also}, \\ 2y-7=3y-2 \\ \Rightarrow 2y-3y=-2+7 \\ \Rightarrow -y=5 \\ \Rightarrow y=-5 \\ z+4=6 \\ \Rightarrow z=6-4 \\ \Rightarrow z=2 \\ a-1=-3 \\ \Rightarrow a=-3+1 \\ \Rightarrow a=-2 \\ 3b=-21 \\ \Rightarrow b=-7 \\ z+2c=0 \\ \Rightarrow 2=-2c \\ \Rightarrow c=-1 \end{gathered}$$

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