Question

If \(\left| {\begin{array}{*{20}{c}} {2a + b + c}&{a + 2b + c}&{a + b + 2c} \\ {a + 2b + c}&{a + b + 2c}&{2a + b + c} \\ {a + b + 2c}&{2a + b + c}&{a + 2b + c} \end{array}} \right| = \lambda \left| {\begin{array}{*{20}{c}} a&b&c \\ b&c&a \\ c&a&b \end{array}} \right|\), then the value of λ is
1. 4
2. -4
3. 0
4. 4(a + b + c)

Answer 1

Correct Answer - Option 1 : 4
\(\Delta = \left| {\begin{array}{*{20}{c}} {2a + b + c}&{a + 2b + c}&{a + b + 2c} \\ {a + 2b + c}&{a + b + 2c}&{2a + b + c} \\ {a + b + 2c}&{2a + b + c}&{a + 2b + c} \end{array}} \right| = --\left| {\begin{array}{*{20}{c}} 1&1&0 \\ 1&0&1 \\ 0&1&1 \end{array}} \right|\,\left| {\begin{array}{*{20}{c}} {a + b}&{b + c}&{c + a} \\ {b + c}&{c + a}&{a + b} \\ {c + a}&{a + b}&{b + c} \end{array}} \right| \Rightarrow \lambda = 4\)