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NDA 2013
Exam
NDA
Year
2013
Subject
Mathematics
Chapter
Determinants

NDA 2013 · Mathematics · Determinants

The cofactor of the element 4 in the determinant | array lll 1 & 2...

The cofactor of the element 4 in the determinant \left|123456589\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 5 & 8 & 9\end{array}$\right| is$

Options

  1. A2
  2. B4
  3. C6
  4. D–6

Correct answer

C. 6

Step-by-step solution

The co-factor of an element a_{i j} of det⁡A\operatorname{det} \mathrm{A} is equal to (−1)i+j(-1)^{i+j} times its minor. Co-factor Cij=(−1)i+jMijC21=(−1)2+1∣2389∣=−1(18−24)=6\begin{aligned} \mathrm{C}_{i j} & =(-1)^{i+j} \mathrm{M}_{i j} \\ \mathrm{C}_{21} & =(-1)^{2+1}\left|\begin{array}{ll} 2 & 3 \\ 8 & 9 \end{array}\right| \\ & =-1(18-24)=6 \end{aligned}
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