Question

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

(a) -6

(b) -34

(c) 34

(d) 22

The question was asked at a job interview.

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

Answer 1

Right option is (b) -34

To explain I would say: ∆=\(\begin{vmatrix}1&1&-2\\3&4&5\\-1&2&1\end{vmatrix}\)

Expanding along the first row, we get

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

=1(4-5(2))-1(3-5(-1))-2(6-4(-1))

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

=-6-8-20=-34.