Question

Evaluate \(\begin{vmatrix}1&0&1\\0&0&1\\1&0&1\end{vmatrix}\).

(a) 2

(b) 0

(c) 1

(d) -1

I got this question in an international level competition.

My query is from Determinant topic in division Determinants of Mathematics – Class 12

Answer 1

Right option is (b) 0

The best I can explain: Δ=\(\begin{vmatrix}1&0&1\\0&0&1\\1&0&1\end{vmatrix}\)

Δ=1\(\begin{vmatrix}0&1\\0&1\end{vmatrix}\)-0\(\begin{vmatrix}0&1\\1&1\end{vmatrix}\)+1\(\begin{vmatrix}0&0\\1&0\end{vmatrix}\)

Δ=1(0-0)-0(0-1)+1(0-0)

Δ=0-0+0=0.