![Example 21 - Verify (AB)’ = B’A’ if A = [-2 4 5] B = [1 3 -6]](https://d77da31580fbc8944c00-52b01ccbcfe56047120eec75d9cb2cbd.ssl.cf6.rackcdn.com/0ddcb76d-2dd1-4928-876c-31b890bb304e/slide56.jpg)
Learn in your speed, with individual attention - Teachoo Maths 1-on-1 Class
Example 21 - Chapter 3 Class 12 Matrices
Last updated at May 29, 2023 by Teachoo
Chapter 3 Class 12 Matrices
Concept wise
- Formation and order of matrix
- Types of matrices
- Equal matrices
- Addition/ subtraction of matrices
- Statement questions - Addition/Subtraction of matrices
- Multiplication of matrices
- Statement questions - Multiplication of matrices
- Solving Equation
- Finding unknown - Element
- Finding unknown - Matrice
-
Transpose of a matrix
- Symmetric and skew symmetric matrices
- Proof using property of transpose
- Inverse of matrix using elementary transformation
- Proof using mathematical induction
Transcript
Example 21 If A =[■8(−[email protected]@5)], B = [1 3 -6], verify that (AB)’ = B’A’ Taking L.H.S Finding AB AB = [■8(−[email protected]@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&[email protected]&12&−[email protected]&15&−30)] AB = [■8(−2&−6&[email protected]&12&−[email protected]&15&−30)] Now, (AB)’ = [■8(−2&4&5@−6&12&[email protected]&−24&−30)] Taking R.H.S B’ A’ Finding B’ Given B = "[1 3 −6]" B’ = 〖"[1 3 −6]" 〗^′ = [■8([email protected]@−6)] Now, A = [■8(−[email protected]@5)] A’ = [■8(−[email protected]@5)]^′= [ −2 4 5] Finding B’A’ B’ A’ = [■8([email protected]@−6)]_(3×1) 〖"[ −2 4 5]" 〗_(1×3) = [■8(1 × (−2)&1 × 4 &1 × [email protected] × (−2)&3 × 4&3 × 5@−6 × (−2)&−6 × 4&−6 × 5)]_(3×3) = [■8(−2&4&5@−6&12&[email protected]&−24&−30)] = L.H.S Hence L.H.S = R.H.S Hence proved
