Question

If $\begin{bmatrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \end{bmatrix}$ is a singular matrix, then x is

• A. $\frac{13}{25}$
• B. $-\frac{25}{13}$
• C. $\frac{5}{13}$
• D. $\frac{25}{13}$

Hint:

Singular matrix has determinant zero.

Answer 1

The Correct Option is D

Step 1: Singular matrix means determinant = 0. $\begin{vmatrix} 2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5 \end{vmatrix} = 0$.}
Step 2: Expand: $(2+x)(5-2) - 3(-5-2x) + 4(1+x) = (2+x)(3) - 3(-5-2x) + 4(1+x) = 6+3x +15+6x +4+4x = 25+13x = 0 \Rightarrow x = -\frac{25}{13}$.}