Question

For what value of x, the matrix $\begin{bmatrix} 3 - x & 2 & 2 \ 2 & 4 - x & 1 \

• 2 & - 4 & - 1 - x \end{bmatrix}$ is singular.

• A. x = 1, 2
• B. x = 0, 2
• C. x = 0, 1
• D. x = 0, 3.

Answer 1

Answer: (D)

x = 0, 3.

Answer 2

Since, the given matrix is singular

$\Rightarrow \left| \begin{matrix} 3 - x & 2 & 2 \ 2 & 4 - x & 1 \

• 2 & - 4 & - 1 - x \end{matrix} \right| = 0$R₂ +$R_{3}$

$\Rightarrow \left| \begin{matrix} 3 - x & 2 & 2 \ 0 & - x & - x \

• 2 & - 4 & - 1 - x \end{matrix} \right| = 0$$\Rightarrow x\left| \begin{matrix} 3 - x & 2 & 2 \ 0 & 1 & 1 \ 2 & 4 & 1 + x \end{matrix} \right| = 0$

$\Rightarrow$ x {(3 – x) (1 + x – 4) – o + 2 (2 – 2)} = 0

$\Rightarrow$ x (3 – x) (x – 3) = 0 $\Rightarrow$ x = 0, 3