Question

For which of the elements in the determinant Δ=\(\begin{vmatrix}1&8&-6\\2&-3&4\\-7&9&5\end{vmatrix}\) the cofactor is -37.

(a) 4

(b) 1

(c) -6

(d) -3

I had been asked this question during an interview for a job.

This intriguing question comes from Determinants in chapter Determinants of Mathematics – Class 12

Answer 1

The correct option is (d) -3

To elaborate: Consider the element -3 in Δ=\(\begin{vmatrix}1&8&-6\\2&-3&4\\-7&9&5\end{vmatrix}\)

The cofactor of the element -3 is given by

A22=(-1)^2+2 M22

M22=\(\begin{vmatrix}1&-6\\-7&5\end{vmatrix}\)=1(5)-(-6)(-7)=5-42=-37

A22=(-1)^2+2 (-37)=-37.