Question

Evaluate \(\begin{vmatrix}5&4&3\\3&4&1\\5&6&1\end{vmatrix}\).

(a) 4

(b) -24

(c) -8

(d) 8

This question was posed to me by my school teacher while I was bunking the class.

Origin of the question is Determinant in chapter Determinants of Mathematics – Class 12

Answer 1

The correct answer is (c) -8

The explanation: Expanding along the first row, we get

∆=5\(\begin{vmatrix}4&1\\6&1\end{vmatrix}\)-4\(\begin{vmatrix}3&1\\5&1\end{vmatrix}\)+3\(\begin{vmatrix}3&4\\5&6\end{vmatrix}\)

=5(4-6)-4(3-5)+3(18-20)

=5(-2)-4(-2)+3(-2)=-10+8-6=-8.