Value of a Determinant

Value of a Determinant

Δ = = for each i.

Also Δ = .

Note: is called expansion of Δ w.r.t its ith row. Expansion w.r.t each row gives the same value and is called value of Δ.

Application 2 Find  the value of .

Solution M₁₁ = = 8, M₁₂ = = 3 and M₁₃ = = −4.

∴ = 2M₁₁ − 3M₁₂ + M₁₃ = 2 × 8 − 3 × 3 + 1 × (−4) = 3