Q257 / 270 · NDA 2013 (Phase 2) · Mathematics

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

  • A
    2
  • B
    4
  • Correct answer
    C
    6
  • D
    –6

Solution

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

Hence, the correct answer is option: 'C'.

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