Question

Find the value of the determinant in which elements of the first row are 2√3 , 9 and elements of the second row are 2 , 3√3 *

Answer 1

Answer:

Property 1

The value of the determinant remains unchanged if both rows and columns are interchanged.

Verification: Let

Properties of Determinants

Expanding along the first row, we get,

Properties of Determinants

= a1 (b2 c3 – b3 c2) – a2 (b1 c3 – b3 c1) + a3 (b1 c2 – b2 c1)

By interchanging the rows and columns of Δ, we get the determinant

Properties of Determinants

Expanding Δ1 along first column, we get,

Δ1 = a1 (b2 c3 – c2 b3) – a2 (b1 c3 – b3 c1) + a3 (b1 c2 – b2 c1)

Hence Δ = Δ1

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