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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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Transcript

Question 2 Using the property of determinants and without expanding, prove that: |■8(a−b&b−c&c−𝑎@b−c&c−a&a−[email protected]−a&a−b&b−c)| = 0 |■8(a−b&b−c&c−𝑎@b−c&c−a&a−[email protected]−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−[email protected]−c&c−a&a−[email protected]−a&a−b&b−c)| = |■8(0&0&[email protected]−c&c−a&a−[email protected]−a&a−b&b−c)| = 0 |■8(c−a&a−[email protected]−b&b−c)| – 0 |■8(b−c&a−[email protected]−a&b−c)| + 0 |■8(b−c&c−[email protected]−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 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.