Last updated at Aug. 18, 2021 by Teachoo

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Ex 4.2, 8 By using properties of determinants, show that: (i) |โ 8(1&๐&๐2@1&๐&๐2@1&๐&๐2)| = (a - b) (b - c)(c โ a) Solving L.H.S |โ 8(1&๐&๐2@1&๐&๐2@1&๐&๐2)| Applying R1 โ R1 โ R2 = |โ 8(๐โ๐&๐โ๐&๐^2โ๐^2@1&๐&๐2@1&๐&๐2 ) | = |โ 8(๐&(๐โ๐)&(๐โ๐)(๐+๐)@1&๐&๐2@1&๐&๐2 ) | = |โ 8(0(๐โ๐)&(๐โ๐)&(๐โ๐)(a+b)@1&b&b2@1&c&c2 ) | Taking Common (a โ b) from R1 = (๐โ๐) |โ 8(0&1&a+b@1&b&b2@1&c&c2 ) | Applying R2 โ R2 โ R3 = (aโb) |โ 8(0&1&a+b@๐โ๐&bโc&b2โc2@1&c&c2 ) | = (a โ b) |โ 8(0&1&a+๐@๐&bโc&(bโc)(b+c)@1&c&c2 ) | Taking common (b โ c) from R2 = (a โ b) (b โ c) |โ 8(0&1&a+b@0&1&b+c@1&c&c2 ) | Expanding Determinant along C1 = (a โ b) (b โ c) ( 0|โ 8(1&๐+๐@๐&๐2)|โ0|โ 8(1&๐+๐@๐&๐2)|+1|โ 8(1&๐+๐@1&๐+๐)|) = (a โ b) (b โ c) ( 0โ0+1|โ 8(1&๐+๐@1&๐+๐)|) = (a โ b) (b โ c) (1(b + c) โ 1(a + b) ) = (a โ b) (b โ c) (b + c โ a โ b) = (a โ b) (b โ c)(c โ a) = R.H.S Hence Proved

Ex 4.2

Ex 4.2, 1
Deleted for CBSE Board 2022 Exams

Ex 4.2, 2 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 3 Deleted for CBSE Board 2022 Exams

Ex 4.2, 4 Deleted for CBSE Board 2022 Exams

Ex 4.2, 5 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 6 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 7 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 8 (i) Important Deleted for CBSE Board 2022 Exams You are here

Ex 4.2, 8 (ii) Deleted for CBSE Board 2022 Exams

Ex 4.2, 9 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 10 (i) Deleted for CBSE Board 2022 Exams

Ex 4.2, 10 (ii) Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 11 (i) Deleted for CBSE Board 2022 Exams

Ex 4.2, 11 (ii) Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 12 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 13 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 14 Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 15 (MCQ) Important Deleted for CBSE Board 2022 Exams

Ex 4.2, 16 (MCQ) Deleted for CBSE Board 2022 Exams

Chapter 4 Class 12 Determinants (Term 1)

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Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 10 years. He provides courses for Maths and Science at Teachoo.