# Ex 4.2, 11 (ii) - Chapter 4 Class 12 Determinants (Term 1)

Last updated at Aug. 18, 2021 by

Last updated at Aug. 18, 2021 by

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Ex 4.2, 11 By using properties of determinants, show that: (ii) |โ 8(x+y+2z&x&y@z&y+z+2x&y@z&x&z+x+2y)| = 2(x + y + z)3 Solving L.H.S |โ 8(x+y+2z&x&y@z&y+z+2x&y@z&x&z+x+2y)| Applying C1 โ C1 + C2 + C3 = |โ 8(๐ฅ+๐ฆ+2๐ง+๐ฅ+๐ฆ&๐ฅ&๐ฆ@๐ง+๐ฆ+๐ง+2๐ฅ+๐ฆ&๐ฆ+๐ง+2๐ฅ&๐ฆ@๐ง+๐ฅ+๐ง+๐ฅ+2๐ฆ&๐ฅ&๐ง+๐ฅ+2๐ฆ)| = |โ 8(๐(๐+๐+๐)&๐ฅ&๐ฆ@๐(๐+๐+๐)&y+๐ง+2๐ฅ&y@๐(๐+๐+๐)&x&z+x+2y)| Taking common 2(๐ฅ+๐ฆ+๐ง) from C1 = ๐(๐ฑ+๐ฒ+๐ณ) |โ 8(1&๐ฅ&๐ฆ@1&y+๐ง+2๐ฅ&y@1&x&z+x+2y)| Applying R2 โ R2 โ R3 = 2(x+y+z)|โ 8(1&๐ฅ&๐ฆ@๐โ๐&y+๐ง+2๐ฅโ๐ฅ&yโ(๐ง+๐ฅ+2๐ฆ)@1&x&z+x+2y)| = 2(x+y+z)|โ 8(1&๐ฅ&๐ฆ@๐&๐ฅ+๐ฆ+๐ง&โ๐ฅโ๐ฆโ๐ง@1&x&z+x+2y)| = 2(x+y+z)|โ 8(1&๐ฅ&๐ฆ@0&(๐+๐+๐)&โ(๐+๐+๐)@1&x&z+x+2y)| Taking common (๐ฅ+๐ฆ+๐ง) from 2nd Row = 2(x+y+z)(x+y+z)|โ 8(1&๐ฅ&๐ฆ@0&1&โ1@1&x&z+x+2y)| Applying R3 โ R3 โ R1 = 2(x+y+z)2|โ 8(1&๐ฅ&๐ฆ@0&1&โ1@๐โ๐&xโ๐ฅ&z+x+2yโy)| = 2(x+y+z)2|โ 8(1&๐ฅ&๐ฆ@0&1&โ1@๐&0&x+y+z)| Taking common (๐ฅ+๐ฆ+๐ง) Common from 3rd Row = 2(x+y+z)2(x+y+z)|โ 8(1&๐ฅ&๐ฆ@0&1&โ1@0&0&1)| Expanding Determinant along C1 = 2(x+y+z)3 ( 1|โ 8(1&โ1@0&1)|โ0|โ 8(๐ฅ&๐ฆ@0&1)|+0|โ 8(x&y@1&โ1)|) = 2(x+y+z)3 ( 1|โ 8(1&โ1@0&1)|โ0+0) = 2(x+y+z)3 (1(1โ0)โ๐ฅ(0)+๐ฆ(0)) = 2(x+y+z)3 (1) = 2(x+y+z)3 = 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

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 You are here

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.