Answer :

Let Δ =

Applying Row Transformations

R_{2}→ R_{2} – R_{1}

Δ =

R_{3}→ R_{3} – R_{1}

Δ =

Taking (β – α)(γ – α) from R_{2} and R_{3} respectively

Δ = (β – α) (γ – α)

Applying R_{3}→ R_{3} – R_{2}, we have

Δ = (β – α) (γ – α)

Expanding along R_{3}, we have

Δ = (β – α) (γ – α) [0 (α^{2} × (-1) – (β + γ) × (β + γ) – (γ – β)((-1) × α – 1 × (β + γ) + 0 (α × (β + γ) – 1 × α^{2})

Δ = (β – α) (γ – α) [0 – (γ – β)( - α - β – γ) + 0]

Δ = (β – α) (γ – α) (γ – β) (α + β + γ)

Δ = (α – β) (β – γ) (γ – α) (α + β + γ)

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