If x & 1 & 1 2 & 3 & 4 1 & 1 & 1 has no i… - Vidyadip

MCQ

If $\begin{bmatrix}\text{x} &\text{amp; } 1 &\text{amp; 1}\\ 2 &\text{amp; 3} &\text{amp; 4}\\ 1 &\text{amp; 1} &\text{amp; 1}\end{bmatrix}$ has no inverse, then $\text{x}=$

A
$-4$
B
$-2$
✓
$1$
D
$-3$

✓

Answer

Correct option: C.

$1$

We know that, If Dett $= 0$ there is no inverse
$\Rightarrow D = x(3 - 4) - 1(2 - 4) + 1(2 - 3) = 0$
$\Rightarrow -x + 2 - 1 = 0$
$\Rightarrow x = 1$

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