Question

Find the cofactor of element -3 in the determinant Δ=\(\begin{vmatrix}1&4&4\\-3&5&9\\2&1&2\end{vmatrix}\).

(a) -4

(b) 4

(c) -5

(d) -3

This question was posed to me in my homework.

Origin of the question is Determinants in section Determinants of Mathematics – Class 12

Answer 1

Right option is (a) -4

Explanation: The minor of element -3 is given by

M21=\(\begin{vmatrix}4&4\\1&2\end{vmatrix}\)=4(2)-4=4 (Obtained by eliminating R2 and C1)

∴A21=(-1)^2+1 M21=(-1)^3 4=-4.