![Example 21 - Verify (AB)’ = B’A’ if A = [-2 4 5] B = [1 3 -6]](https://d1avenlh0i1xmr.cloudfront.net/0ddcb76d-2dd1-4928-876c-31b890bb304e/slide56.jpg)
Example 21 - Chapter 3 Class 12 Matrices (Term 1)
Last updated at Jan. 17, 2020 by Teachoo
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
Examples
Example 1
Example 2
Example 3
Example 4
Example 5 Important
Example 6
Example 7
Example 8
Example 9
Example 10
Example 11
Example 12
Example 13
Example 14
Example 15
Example 16
Example 17
Example 18 Important
Example 19
Example 20 Important
Example 21 You are here
Example 22 Important
Example 23 Deleted for CBSE Board 2022 Exams
Example 24 Important Deleted for CBSE Board 2022 Exams
Example 25 Important Deleted for CBSE Board 2022 Exams
Example 26 Important
Example 27 Important
Example 28
Chapter 3 Class 12 Matrices (Term 1)
Serial order wise
About the Author
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.