Question

The value of $\begin{vmatrix} b+c&a&a\\\ b &c+a &b\\\ c & c &a+b \end{vmatrix}$ is

• A. abc
• B. (a + b) (b + c) (c + a)
• C. 4abc
• D. none of these

Answer 1

Answer: (C)

4abc

Answer 2

Operate $R_1 - R_2 - R_3$, we get the given det. $\begin{vmatrix}0 &-2c&-2b\\\ b &c+a&b\\\ c&c&a+b\end{vmatrix} = 4 abc$ (on simplification).