Question

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

• A. $a + b + c$
• B. $(a + b + c)^{2}$
• C. 0
• D. $1 + a + b + c$

Answer 1

Answer: (C)

0

Answer 2

$\Delta = \left| \begin{matrix} 1 & a & b + c \\ 1 & b & c + a \\ 1 & c & a + b \end{matrix} \right| = (a + b + c)\left| \begin{matrix} 1 & 1 & b + c \\ 1 & 1 & c + a \\ 1 & 1 & a + b \end{matrix} \right|$

$(C_{2} \rightarrow C_{2} + C_{3})$

= 0, $(\because C_{1} \equiv C_{2})$.