If the matrix 1 &3& amp +2 2& amp;4&8 3&5&10 is s… - Vidyadip

MCQ

If the matrix $\begin{bmatrix}1 &\text{amp;3}& \text{amp}\lambda+2 \\2& \text{amp;4}&\text{amp;8} \\3&\text{amp;5}&\text{amp;}10 \end{bmatrix}$ is singular, then $\lambda=$

A
$-2$
B
$4$
✓
$2$
D
$-4$

✓

Answer

Correct option: C.

$2$

A matrix is singular if and only if it has a determinant of $0.$
$\begin{bmatrix}1 &\text{amp;3}& \text{amp}\lambda+2 \\2& \text{amp;4}&\text{amp;8} \\3&\text{amp;5}&\text{amp;}10 \end{bmatrix}$
$(40-40)-2(20-24)+(\lambda+2)(10-12)=0$
$2\lambda=4$
$\Rightarrow\lambda=2$

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