Answer :

Let Δ =

Applying Row Transformations


R2 R2 – R1


Δ =


R3 R3 – R1


Δ =


Taking (β – α)(γ – α) from R2 and R3 respectively


Δ = (β – α) (γ – α)


Applying R3 R3 – R2, we have


Δ = (β – α) (γ – α)


Expanding along R3, we have


Δ = (β – α) (γ – α) [0 (α2 × (-1) – (β + γ) × (β + γ) – (γ – β)((-1) × α – 1 × (β + γ) + 0 (α × (β + γ) – 1 × α2)


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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