# Ex 4.2, 14 - Chapter 4 Class 12 Determinants (Term 1)

Last updated at Jan. 22, 2020 by Teachoo

Last updated at Jan. 22, 2020 by Teachoo

Transcript

Ex 4.2, 14 By using properties of determinants, show that: |โ 8(a2+1&ab&ac@ab&b2+1&bc@ca&cb&c2+1)| = 1 + a2 + b2 + c2 Solving L.H.S |โ 8(a2+1&ab&ac@ab&b2+1&bc@ca&cb&c2+1)| Multiplying & Dividing by abc = ๐๐๐/๐๐๐ |โ 8(a2+1&ab&ac@ab&b2+1&bc@ca&cb&c2+1)| Multiplying 1st row by a, 2nd row by b & 3rd row by c ( R1 โ aR1 , R2 โ bR3 , R3 โ bR3 ) = 1/๐๐๐ |โ 8(๐(a2+1)&๐(ab)&๐(ac)@๐(ab)&๐(b2+1)&๐(bc)@๐(ca)&๐(cb)&๐(c2+1))| = 1/๐๐๐ |โ 8(a3+a&๐2b&๐2c@ab2&b3+b&๐2c@c2a&๐2b&c3+c)| Applying R1 โ R1 + R2 + R3 = 1/๐๐๐ |โ 8(a3+a+๐๐2+๐2๐&๐2b+b3+b+c2b&๐2c+b2c+c3+c@ab2&b3+b&๐2c@c2a&๐2b&c3+c)| = 1/๐๐๐ |โ 8(a(๐๐+๐+๐๐+๐๐)&๐(๐๐+๐๐+๐+๐๐)&๐(๐๐+๐๐+๐๐"+1" )@ab2&b3+b&๐2c@c2a&๐2b&c3+c)| Taking (1+๐2+๐2+๐2) common from 1st Row = ((๐ + ๐๐ + ๐๐ + ๐๐))/๐๐๐ |โ 8(a&๐&๐@ab2&b3+b&๐2c@c2a&๐2b&c(c3+1))| Taking a common from C1 ,b from C2 & c from C3 . = ๐๐๐ ( (1 + ๐2 + ๐2 + ๐2))/๐๐๐ |โ 8(1&1&1@b2&b3+1&๐2@c2&๐2&c2+1)| Applying C1 โ C1 โ C2 = (1+๐2+๐2+๐2) |โ 8(๐โ๐&1&1@b2โ๐2โ1&b2+1&๐2@c2โc2&๐2&c2+1)| = (1+๐2+๐2+๐2) |โ 8(๐&1&1@โ1&b2+1&๐2@0&๐2&c2+1)| Applying C2 โ C2 โ C3 = (1+๐2+๐2+๐2) |โ 8(0&๐โ๐&1@โ1&b2+1โ๐2&๐2@0&๐2โ๐2โ1&c2+1)| = (1+๐2+๐2+๐2) |โ 8(0&๐&1@โ1&1&๐2@0&โ1&c2+1)| Expanding along R1 = (1+๐2+๐2+๐2)(1|โ 8(1&๐2@โ1&๐2+1)|" โ 0" |โ 8(โ1&๐ถ2@0&๐2+1)|" + 0" |โ 8(1&1@0&โ1)|) = (1 + a2 + b1 + c2) (0 โ 0 + 1) = (1 + a2 + b1 + c2) (1) = (1 + a2 + b1 + c2) = 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

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 You are here

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.