Question

\(\begin{vmatrix} a + b + 2c & a & b \\[0.3em] c&b + c + 2a & b \\[0.3em] c & a &c + a +2b \end{vmatrix}\) = 2(a + b + c)³

Answer 1

On applying C₁ → C₁ + C₂ + C₃

Take 2(a + b + c) common

On applying R₂ → R₂ - R_1, and R₃ → R₃ - R₁

So,

Hence proved.