Question

Find $x,y$ and $z$, so that $A=B$, where
$A=\left[\begin{array}{ccc}x-2& 3& 2z\\ 18z& y+2& 6z\end{array}\right],B=\left[\begin{array}{ccc}y& z& 6\\ 6y& x& 2y\end{array}\right]$

Answer 1

It is given that, $A=B$

$\left[\begin{array}{ccc}x-2& 3& 2z\\ 18z& y+2& 6z\end{array}\right]=\left[\begin{array}{ccc}y& z& 6\\ 6y& x& 2y\end{array}\right]$

Since, matrices are equal then, their corresponding elements are also equal.

$\Rightarrow$ $x-2=y$

$\Rightarrow$ $3=z$ ---- ( 1 )

$\Rightarrow$ $2z=6$

$\Rightarrow$ $18z=6y$ ---- ( 2 )

$\Rightarrow$ $y+2=x$ ----- ( 3 )

$\Rightarrow$ $6z=2y$

From ( 1 ) we get,

$\Rightarrow$ $z=3$

Substituting $z=3$ in equation ( 2 ) we get,

$\Rightarrow$ $18\left(3\right)=6y$

$\Rightarrow$ $54=6y$

$\Rightarrow$ $y=\frac{54}{6}$

$\therefore$ $y=9$

Substituting $y=9$ in equation ( 3 ) we get,

$\Rightarrow$ $x=9+2$

$\therefore$ $x=11$

$\Rightarrow$ $x=11,y=9$ and $z=3$