Question

Find the minor and cofactor respectively for the element 3 in the determinant Δ=\(\begin{vmatrix}1&5\\3&6\end{vmatrix}\).

(a) M21=-5, A21=-5

(b) M21=5, A21=-5

(c) M21=-5, A21=5

(d) M21=5, A21=5

The question was asked during a job interview.

The question is from Determinants in chapter Determinants of Mathematics – Class 12

Answer 1

Correct choice is (b) M21=5, A21=-5

The best explanation: The element 3 is in the second row (i=2) and first column(j=1).

∴M21=5 (obtained by deleting R2 and C1 in Δ)

A21=(-1)^1+2 M21=-1×5 =-5.