Check sibling questions

Example 21 - Verify (AB)’ = B’A’ if A = [-2 4 5] B = [1 3 -6]

Example 21 - Chapter 3 Class 12 Matrices - Part 2
Example 21 - Chapter 3 Class 12 Matrices - Part 3
Example 21 - Chapter 3 Class 12 Matrices - Part 4

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Transcript

Example 21 If A =[■8(−2@4@5)], B = [1 3 -6], verify that (AB)’ = B’A’ Taking L.H.S Finding AB AB = [■8(−2@4@5)]_(3 × 1) 〖"[1 3 −6]" 〗_(1 × 3) = [■8(−2 × 1&−2 × 3&−2 × (−6)@4 × 1&4 × 3&4 × (−6)@5 × 1&5 × 3&5 × (−6))]_(3 × 3) = [■8(−2&−6&12@4&12&−24@5&15&−30)] AB = [■8(−2&−6&12@4&12&−24@5&15&−30)] Now, (AB)’ = [■8(−2&4&5@−6&12&15@12&−24&−30)] Taking R.H.S B’ A’ Finding B’ Given B = "[1 3 −6]" B’ = 〖"[1 3 −6]" 〗^′ = [■8(1@3@−6)] Now, A = [■8(−2@4@5)] A’ = [■8(−2@4@5)]^′= [ −2 4 5] Finding B’A’ B’ A’ = [■8(1@3@−6)]_(3×1) 〖"[ −2 4 5]" 〗_(1×3) = [■8(1 × (−2)&1 × 4 &1 × 5@3 × (−2)&3 × 4&3 × 5@−6 × (−2)&−6 × 4&−6 × 5)]_(3×3) = [■8(−2&4&5@−6&12&15@12&−24&−30)] = L.H.S Hence L.H.S = 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 12 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.