Ex 4.2, 2 - Chapter 4 Class 12 Determinants

Transcript

Ex 4.2, 2 Using the property of determinants and without expanding, prove that: |■8(a−b&b−c&c−𝑎@b−c&c−a&a−b@c−a&a−b&b−c)| = 0 |■8(a−b&b−c&c−𝑎@b−c&c−a&a−b@c−a&a−b&b−c)| Making first row 0 by Applying R1 →R1 + R2 + R3 = |■8(a−b+b−c+c−a&b−c+c−a+a−b&c−a+a−b+b−c@b−c&c−a&a−b@c−a&a−b&b−c)| = |■8(0&0&0@b−c&c−a&a−b@c−a&a−b&b−c)| = 0 |■8(c−a&a−b@a−b&b−c)| – 0 |■8(b−c&a−b@c−a&b−c)| + 0 |■8(b−c&c−a@c−a&a−b)| = 0 – 0 + 0 = 0 = R.H.S Thus, L.H.S = R.H.S Hence proved