Question

Evaluate:

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

Answer 1

Suppose

On applying column operation C₂ → C₂ + C₁

On taking (a + b + c) common

On applying row operation R₂ → R₂ - R₁ and R₃ → R₃ - R₁ 

On taking (b - c) and (c - a) common

= (a + b + c) (b – a) (c – a) (b – c)

Therefore, Δ = (a + b + c) (b – a) (c – a) (b – c)