Browse Questions

# Evaluate : $\begin{vmatrix}0 &a-b&b-c\\b-a&0&b-c\\c-a&c-b&0\end{vmatrix}$

(A) 1 (B) 2 (C) 3 (D) 0
Can you answer this question?

Applying $R_1 \rightarrow R_1-R_2$
$R_2\rightarrow R_2-R_3$
We get,
$\begin{vmatrix}a-b&a-b&a-b\\b-c&b-c&b-c\\c-a&c-b&0\end{vmatrix}$
$\Rightarrow (a-b)(b-c)\begin{vmatrix}1&1&1\\1&1&1\\c-a&c-b&0\end{vmatrix}$
$\Rightarrow 0$
Hence (d) is the correct answer.
answered Nov 19, 2013