Question

For which of the following element in the determinant Δ=\(\begin{vmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{vmatrix}\) , the minor and the cofactor both are zero.

(a) -5

(b) 2

(c) -6

(d) 8

The question was posed to me in an online interview.

The doubt is from Determinants topic in division Determinants of Mathematics – Class 12

Answer 1

Right answer is (b) 2

For explanation: Consider the element 2 in the determinant Δ=\(\begin{vmatrix}5&-5&8\\6&2&-1\\5&-6&8\end{vmatrix}\)

The minor of the element 2 is given by

∴M22=\(\begin{vmatrix}5&8\\5&8\end{vmatrix}\)=40-40=0

⇒A22=(-1)^2+2 (0)=0.