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NDA 2023
Exam
NDA
Year
2023
Subject
Mathematics
Chapter
Determinants

NDA 2023 · Mathematics · Determinants

If | array ccc x^2-3 x & x-1 & x+3 x+1 & -2 x & x-4 x-3 & x+4 & 3 x...

If \left|x2−3xx−1x+3x+1−2xx−4x−3x+43x\begin{array}{ccc}x^2-3 x & x-1 & x+3 \\ x+1 & -2 x & x-4 \\ x-3 & x+4 & 3 x\end{array}$\right|=a x^4+b x^3+c x^2+d x+e, then what is the value of ee ?$

Options

  1. A-1
  2. B0
  3. C1
  4. D2

Correct answer

B. 0

Step-by-step solution

If we put x=0\left|0−1310−4−340\begin{array}{ccr} 0 & -1 & 3 \\ 1 & 0 & -4 \\ -3 & 4 & 0 \end{array}\right|=0+0+0+0+\mathrm{e} it is skew-symmetric of order3 \times 3\Rightarrow  So, \text{ So, } \quad e=0\mathrm{e}=0
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