Question

What is the minor of the element 5 in the determinant Δ=\(\begin{vmatrix}1&5&4\\2&3&6\\7&9&4\end{vmatrix}\)?

(a) -34

(b) 34

(c) -17

(d) 21

This question was addressed to me in unit test.

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

Answer 1

The correct choice is (a) -34

To elaborate: The minor of element 5 in the determinant Δ=\(\begin{vmatrix}1&5&4\\2&3&6\\7&9&4\end{vmatrix}\) is the determinant obtained by deleting the row and column containing element 5.

∴M12=\(\begin{vmatrix}2&6\\7&4\end{vmatrix}\)=2(4)-7(6)=-34.