Question

b + c & a & a \\ b & c + a & b \\ c & c & a + b \end{matrix} \right| =$$

• A. $abc$
• B. $2abc$
• C. $3abc$
• D. $4abc$

Answer 1

Answer: (D)

$4abc$

Answer 2

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

{by $R_{1} \rightarrow R_{1} - (R_{2} + R_{3})\}$

= $2c.b(a + b - c) - 2b.c(b - c - a) = 4abc$.