Question

$\Delta = \left| \begin{matrix} a + x & b & c \\ b & x + c & a \\ c & a & x + b \end{matrix} \right|$, which of the following is a factor for the above determinant .

• A. $x - (a + b + c)$
• B. $x + (a + b + c)$
• C. $a + b + c$
• D. $- (a + b + c)$

Answer 1

Answer: (B)

$x + (a + b + c)$

Answer 2

Operating $C_{1} \rightarrow C_{1} + C_{2} + C_{3}$

we find that $x + a + b + c$ is a factor.