Question

If \[ \begin{bmatrix} 4 + x & x - 1 \\ -2 & 3 \end{bmatrix} \] is a singular matrix, then the value of \( x \) is:

• A. 0
• B. 1
• C. -2
• D. -4

Hint:

For a matrix to be singular, its determinant must be 0. Always set the determinant to 0 and solve for \( x \).

Answer 1

The Correct Option is C

For a matrix to be singular, its determinant must be 0. The determinant of the given matrix is: \[ \text{det} = (4 + x)(3) - (x - 1)(-2). \] Simplifying: \[ \text{det} = 3(4 + x) + 2(x - 1) = 12 + 3x + 2x - 2 = 14 + 5x. \] Setting the determinant to 0 for the matrix to be singular: \[ 14 + 5x = 0 \quad \Rightarrow \quad 5x = -14 \quad \Rightarrow \quad x = -2. \]