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Example 34 - Chapter 4 Class 12 Determinants (Term 1)

Last updated at March 16, 2023 by

Example 34 - Chapter 4 Class 12 Determinants - Prove that |a + bx

Example 34 - Chapter 4 Class 12 Determinants - Part 2
Example 34 - Chapter 4 Class 12 Determinants - Part 3

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Transcript

Example 34 Prove that Δ = |■8(a+bx&c+dx&[email protected]+b&cx+d&[email protected]&v&w)| = (1 – x2) |■8(a&c&[email protected]&d&[email protected]&v&w)| Solving L.H.S Δ = |■8(a+bx&c+dx&[email protected]+b&cx+d&[email protected]&v&w)| Applying R1 → R1 − xR2 = |■8(𝑎+𝑏𝑥−𝑥 (𝑎𝑥+𝑏)&𝑐+𝑑𝑥−𝑥&𝑝+𝑞𝑥−𝑥 (𝑝𝑥+𝑞)@𝑎𝑥+𝑏&𝑐𝑥+𝑑&𝑝𝑥+𝑞@𝑢&𝑣&𝑤)| = |■8(𝑎+𝑏𝑥−𝑎𝑥2 −𝑏𝑥&𝑐+𝑑𝑥−𝑐𝑥2−𝑑𝑥&𝑝+𝑞𝑥−𝑝𝑥2−𝑝𝑥@𝑎𝑥+𝑏&𝑐𝑥+𝑑&𝑝𝑥+𝑞@𝑢&𝑣&𝑤)| = |■8(a−𝑎𝑥2 &c−cx2&p−[email protected]+b&cx+d&[email protected]&v&w)| = |■8(a (𝟏−𝒙𝟐) &c(𝟏−𝐱𝟐)&p(𝟏−𝐱𝟐)@ax+b&cx+d&[email protected]&v&w)| Taking (1 – x2) common from R1 = (1 – x2) |■8(a&c&[email protected]+b&cx+d&[email protected]&v&w)| Applying R2 → R2 – xR1 = |■8(𝑎+𝑏𝑥−𝑎𝑥2 −𝑏𝑥&𝑐+𝑑𝑥−𝑐𝑥2−𝑑𝑥&𝑝+𝑞𝑥−𝑝𝑥2−𝑝𝑥@𝑎𝑥+𝑏&𝑐𝑥+𝑑&𝑝𝑥+𝑞@𝑢&𝑣&𝑤)| = |■8(a−𝑎𝑥2 &c−cx2&p−[email protected]+b&cx+d&[email protected]&v&w)| = |■8(a (𝟏−𝒙𝟐) &c(𝟏−𝐱𝟐)&p(𝟏−𝐱𝟐)@ax+b&cx+d&[email protected]&v&w)| Taking (1 – x2) common from R1 = (1 – x2) |■8(a&c&[email protected]+b&cx+d&[email protected]&v&w)| Applying R2 → R2 – xR1 = (1 – x2) |■8(𝑎&𝑐&𝑝@𝑎𝑥+𝑏−𝑥𝑎&𝑐𝑥+𝑑−𝑐𝑥&𝑝𝑥+𝑞−𝑝𝑥@𝑢&𝑣&𝑤)| = (1 – x2) |■8(𝑎&𝑐&𝑝@𝑏&𝑑&𝑞@𝑢&𝑣&𝑤)| = R.H.S Hence Proved

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Davneet Singh

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.