Question

If \( AX = B \), where \( A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4 \end{bmatrix} \), \( B = \begin{bmatrix} 1 \\ 2 \end{bmatrix} \) and \( X = \begin{bmatrix} x \\ y \\ z \end{bmatrix} \), then \( x + y + z = \)

• A. 2
• B. 3
• C. 6
• D. 1

Hint:

When solving matrix equations, it is important to use proper methods such as Gaussian elimination or matrix inversion to find the unknowns efficiently.

Answer 1

The Correct Option is B

Step 1: Set up the matrix equation.
We are given the matrix equation \( AX = B \), where: \[ A = \begin{bmatrix} 1 & -1 & 1 \\ 2 & -1 & 0 \\ 3 & 3 & -4 \end{bmatrix}, \quad B = \begin{bmatrix} 1 \\ 2 \end{bmatrix} \] Multiplying matrix \( A \) by \( X \) results in a system of equations.
Step 2: Solve the system.
Solving this system will give the values of \( x \), \( y \), and \( z \). After solving the matrix equation, we find that \( x + y + z = 3 \).
Step 3: Conclusion.
The correct answer is (B) 3.