Question

Find x, y and z so that A = B, where`A= [[x-2,3,2x],[18z,y+2,6x]],``b=[[y,z,6],[6y,x,2y]]`

Answer 1

Since all the corresponding elements of a matrix are equal

 

\[A = \begin{bmatrix}x - 2 & 3 & 2z \\ 18z & y + 2 & 6z\end{bmatrix} , B = \begin{bmatrix}y & z & 6 \\ 6y & x & 2y\end{bmatrix}\]
\[Here, \]
\[x - 2 = y . . . \left( 1 \right) \]
\[z = 3 . . . \left( 2 \right) \]
\[18z = 6y . . . \left( 3 \right)\]
Putting the value of z in eq . (3) , we get
\[18\left( 3 \right) = 6y\]
\[ \Rightarrow 54 = 6y\]
\[ \Rightarrow y = \frac{54}{6} = 9\]  
Putting the value of  y in eq . (1) , we get

\[x - 2 = 9\]
\[ \Rightarrow x = 9 + 2\]
\[ \Rightarrow x = 11\]
`∴x=11 , y=9 ` and `z=3`