Question

In the matrix equation: \[ \begin{bmatrix} 3 & -1 \\ 2 & 5 \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} 4 \\ -3 \end{bmatrix}, \] the values of \( x \) and \( y \) are:

• A. \( x = 3, y = -1 \)
• B. \( x = -1, y = 1 \)
• C. \( x = 1, y = -1 \)
• D. \( x = -1, y = 3 \)

Hint:

For a 2x2 matrix, solving the linear equations directly gives us the values of the variables

Answer 1

The Correct Option is C

We can solve this matrix equation using Gaussian elimination or substitution. The system of equations is: \[ 3x - y = 4, \quad 2x + 5y = -3. \] Solving these equations, we get \( x = 1 \) and \( y = -1 \).