Question 2 - Properties of Determinant - Chapter 4 Class 12 Determinants

Last updated at Dec. 16, 2024 by

Ex 4.2, 2 - Using property of determinants - Class 12 CBSE

Ex 4.2, 2 - Chapter 4 Class 12 Determinants - Part 2

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Question 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

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 14 years. He provides courses for Maths, Science and Computer Science at Teachoo