The matrix 1 & 0 & 1 2 & 1& 0 3 & 1 & 1 i… - Vidyadip

MCQ

The matrix $\begin{bmatrix}1 &\text{amp; } 0 &\text{amp; 1} \\ 2 &\text{amp; 1}&\text{amp; 0} \\ 3 &\text{amp; 1} &\text{amp; 1}\end{bmatrix}$ is:

A
non-singular
✓
singular
C
skew-symmetric
D
symmetric

✓

Answer

Correct option: B.

singular

Given $\text{A}=\begin{bmatrix}1 &\text{amp; } 0 &\text{amp; 1} \\ 2 &\text{amp; 1}&\text{amp; 0} \\ 3 &\text{amp; 1} &\text{amp; 1}\end{bmatrix}$

$\text{|A|}=\begin{bmatrix}1 &\text{amp; } 0 &\text{amp; 1} \\ 2 &\text{amp; 1}&\text{amp; 0} \\ 3 &\text{amp; 1} &\text{amp; 1}\end{bmatrix}$

$\Rightarrow∣\text{A}∣=1−1=0$

Hence, A is singular.

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