Question

Evaluate \(\begin{vmatrix}5&0&5\\1&4&3\\0&8&6\end{vmatrix}\).

(a) 20

(b) 0

(c) -40

(d) 40

This question was addressed to me in an online interview.

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

Answer 1

The correct option is (b) 0

For explanation I would say: Δ=\(\begin{vmatrix}5&0&5\\1&4&3\\0&8&6\end{vmatrix}\)

Expanding along R1, we get

Δ=5\(\begin{vmatrix}4&3\\8&6\end{vmatrix}\)-0\(\begin{vmatrix}1&3\\0&6\end{vmatrix}\)+5\(\begin{vmatrix}1&4\\0&8\end{vmatrix}\)

Δ=5(24-24)-0+5(8-0)

Δ=0-0+40=40.