Question

Solve the following system of equations by using matrix method: \[ 3x - 2y + 3z = 8 \] \[ 2x + y - z = 1 \] \[ 4x - 3y + 2z = 4 \]

Hint:

The matrix method involves writing equations in the form \( AX = B \) and solving using \( X = A^{-1} B \).

Answer 1

The given system of equations can be written in matrix form as: \[ AX = B \] where \[ A = \begin{bmatrix} 3 & -2 & 3 \\ 2 & 1 & -1 \\ 4 & -3 & 2 \end{bmatrix}, \quad X = \begin{bmatrix} x \\ y \\ z \end{bmatrix}, \quad B = \begin{bmatrix} 8 \\ 1 \\ 4 \end{bmatrix}. \] To solve for \( X \), we use: \[ X = A^{-1} B. \] Finding \( A^{-1} \) and computing \( X \), we obtain: \[ x = 3, \quad y = -2, \quad z = 1. \]