Q73 / 170 · Manipal (MET) 2021 · Mathematics

In the determinant $\left|\begin{array}{rrr}3 & x & -1 \\ 2 & -1 & 4 \\ 1 & y & -3\end{array}\right|$, the sum of the cofactors of $x$ and $y$ is

  • A
    -24
  • B
    24
  • Correct answer
    C
    -4
  • D
    4

Solution

Given, determinant $\left|\begin{array}{rrr}3 & x & -1 \\ 2 & -1 & 4 \\ 1 & y & -3\end{array}\right|$ Here, cofactor of $x=10$ and cofactor of $y=-14$ $\therefore$ Their sum $=-4$

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

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