1. Find A^-1 2. Using it solve the system of equations 2x – 3y + 5z = 16, 3x + 2y – 4z = -4, x + y – 2z = -3

Question

If A = \(\begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \)

1.Find A^-1 

2. Using it solve the system of equations 2x – 3y + 5z = 16, 3x + 2y – 4z = -4, x + y – 2z = -3 

Answer 1

1. A = \(\begin{bmatrix} 2 & -3 & 5 \\ 3 & 2 & -4 \\ 1 & 1 & -2 \end{bmatrix} \)

⇒ |A| = 0 + 3x - 2 + 5 = -1

2. Given; 

AX = B
⇒ X = A^-1B

⇒ x = 2, y = 1, z = 3.