Use product [(1,-1,2)(0,2,-3)(3,-2,4)][(-2,0,1)(9,2,-3)(6,1,-2)] to solve the system of equations: x – y + 2z = 1, 2y – 3z = 1, 3x – 2y + 4z = 2

Question

Use product \(\begin{bmatrix} 1 & -1 & 2 \\[0.3em] 0 & 2 & -3 \\[0.3em] 3 & -2& 4 \end{bmatrix}\)\(\begin{bmatrix} -2 &0 & 1 \\[0.3em] 9 & 2 & -3 \\[0.3em] 6 & 1& -2 \end{bmatrix}\) to solve the system of equations: 

x – y + 2z = 1, 2y – 3z = 1, 3x – 2y + 4z = 2

Answer 1

Given system of equations are :

x – y + 2z = 1, 

2y – 3z = 1, 

3x – 2y + 4z = 2

Above system of equations can be written in matrix form as,

AX = B

⇒ X = A^-1 B

Now,

Putting X, A^-1 and B in X = A^-1B, we get