Question

The value of ∆ = $\left| \begin{matrix} 1 & 1 & 1 \\ bc & ca & ab \\ b + c & c + a & a + b \end{matrix} \right|$ is –

• A. 1
• B. (a – b) (b – c)(c – a)
• C. (a + b) (b + c)(c + a)
• D. 0

Answer 1

Answer: (B)

(a – b) (b – c)(c – a)

Answer 2

c₃ → c₃ – c₁, c₂ → c₂ – c₁

∆ = $\left| \begin{matrix} 1 & 0 & 0 \\ bc & c(a–b) & b(a–c) \\ b + c & a–b & a–c \end{matrix} \right|$ = (a – b)(a – c) $\left| \begin{matrix} c & b \\ 1 & 1 \end{matrix} \right|$

= (a – b) (b – c) (c – a)