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NDA 2021
Exam
NDA
Year
2021
Subject
Mathematics
Chapter
Determinants

NDA 2021 · Mathematics · Determinants

If the determinant | array lll x & 1 & 3 0 & 0 & 1 1 & x & 4 array...

If the determinant \left|x130011x4\begin{array}{lll}x & 1 & 3 \\ 0 & 0 & 1 \\ 1 & x & 4\end{array}$\right|=0 then what is xx equal to?$

Options

  1. A-2 or 2
  2. B-3 or 3
  3. C-1 or 1
  4. D3 or 4

Correct answer

C. -1 or 1

Step-by-step solution

\left|x130011x4\begin{array}{lll}x & 1 & 3 \\ 0 & 0 & 1 \\ 1 & x & 4\end{array}\right|=0\Rightarrow x(0-x)+1(1-0)+3(0-0)=0\begin{aligned} & \Rightarrow-x^2+1=0 \\ & \therefore x= \pm 1\end{aligned}$$
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