Question

Evaluate \(\begin{vmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{vmatrix}\)

(a) 100

(b) 223

(c) 240

(d) 230

The question was asked in an internship interview.

Query is from Determinant in chapter Determinants of Mathematics – Class 12

Answer 1

The correct choice is (c) 240

The explanation is: Expanding along R1, we get

Δ=\(\begin{vmatrix}3&-1&3\\6&-5&4\\3&-2&3\end{vmatrix}\)

Δ=3\(\begin{vmatrix}-5&45\\-2&3\end{vmatrix}\)-(-1)\(\begin{vmatrix}6&4\\3&3\end{vmatrix}\)+3\(\begin{vmatrix}6&-5\\3&-2\end{vmatrix}\)

Δ=3(-15+90)+(18-12)+3(-12+15)

Δ=3(75)+6+9=240.