Question

The system of equations

αx + y + z = α – 1

x + αy +z = α – 1

x + y + αz = α – 1

has no solution if α =

• A. – 2
• B. α≠ – 2
• C. Either – 2 or 1
• D. α = 1

Answer 1

Answer: (A)

– 2

Answer 2

∆ = 0 ⇒ $\begin{matrix} \alpha & 1 & 1 \\ 1 & \alpha & 1 \\ 1 & 1 & \alpha \end{matrix}$ = 0

⇒ (α – 1)² (α + 2) = 0

α = 1, – 2

But α ≠ 1 (∴ ∆₁ = ∆₂ =∆₃ = 0)

∴ α = – 2