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Determinants — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsDeterminants1 Mark
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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