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

Question

Find x, y and z so that A = B, where \(A=\begin{bmatrix} x-2 & 3 & 2z \\[0.3em] 18z & y+2 &6z \\[0.3em] \end{bmatrix}, ​​\)\(B=\begin{bmatrix} y & z & 6 \\[0.3em] 6y & z &2y \\[0.3em] \end{bmatrix} ​​\)

Answer 1

Given two matrices are equal as A = B.

 \(\begin{bmatrix} x-2 & 3 & 2z \\[0.3em] 18z & y+2 &6z \\[0.3em] \end{bmatrix} ​​\)\(=\begin{bmatrix} y & z & 6 \\[0.3em] 6y & z &2y \\[0.3em] \end{bmatrix} ​​\) 

We know that if two matrices are equal then the elements of each matrices are also equal.

∴x – 2 = y …(1) 

z = 3 And 

y + 2 = z   … (2) 

2y = 6z 

⇒ y = 3z   …(3)

Putting the value of z in equation (3),

∴ y = 3z 

= 3 × 3 = 9

Putting the value of y in equation (1),

x – 2 = 9 

⇒ x – 2 = 9 

⇒ x = 9 + 2 

⇒ x = 11 

∴ x = 11, 

y = 9,

z = 3.