Question

The value of the determinant $\left| \begin{matrix} 1 & 1 & 1 \\ b + c & c + a & a + b \\ b + c - a & c + a - b & a + b - c \end{matrix} \right|$ is.

• A. abc
• B. $a + b + c$
• C. $ab + bc + ca$
• D. None of these

Answer 1

Answer: (D)

None of these

Answer 2

$\left| \begin{matrix} 1 & 1 & 1 \\ b + c & c + a & a + b \\ b + c - a & c + a - b & a + b - c \end{matrix} \right|$

= $\left| \begin{matrix} 0 & 0 & 1 \\ b - a & c - b & a + b \\ 2(b - a) & 2(c - b) & a + b - c \end{matrix} \right| = 0$.