For the matrices A and B, verify that (AB) ′ =B′ A′ where(i) A=⎣⎡1−43⎦⎤,B=[−121] (ii) A=⎣⎡012⎦⎤,B=[157]

Question

For the matrices A and B, verify that (AB) ′ =B′ A′  where(i) A=⎣⎡​1−43​⎦⎤​,B=[−1​2​1​] (ii) A=⎣⎡​012​⎦⎤​,B=[1​5​7​]

Filo · Accepted Answer

(i) AB=⎣⎡​1−43​⎦⎤​[−1​2​1​]=⎣⎡​−14−3​2−86​1−43​⎦⎤​ ∴(AB) ′ =⎣⎡​−121​4−8−4​−363​⎦⎤​ Now, A′ =[1​−4​3​],B′ =⎣⎡​−121​⎦⎤​ ∴B′ A′ =⎣⎡​−121​⎦⎤​[1​−4​3​]=⎣⎡​−121​4−8−4​−363​⎦⎤​ Hence, we have verified that (AB) ′ =B′ A′ (ii) AB=⎣⎡​012​⎦⎤​[1​5​7​]=⎣⎡​012​0510​0714​⎦⎤​ ∴(AB) ′ =⎣⎡​000​157​21014​⎦⎤​ Now, A′ =[0​1​2​],B′ =⎣⎡​157​⎦⎤​ ∴B′ A′ =⎣⎡​157​⎦⎤​[0​1​2​]=⎣⎡​000​157​21014​⎦⎤​ Hence, we have proved that (AB) ′ =B′ A′

Question Text	For the matrices $A$ and $B$ , verify that $(A B)^{'} = B^{'} A^{'}$ where (i) $A = ⎣ ⎡ 1 - 4 3 ⎦ ⎤, B = [- 1 21]$ (ii) $A = ⎣ ⎡ 012 ⎦ ⎤, B = [157]$
Answer Type	Text solution:1
Upvotes	150

For the matrices $A$ and $B$ , verify that $(A B)^{'} = B^{'} A^{'}$ where
(i) $A = ⎣ ⎡ 1 - 4 3 ⎦ ⎤, B = [- 1 21]$
(ii) $A = ⎣ ⎡ 012 ⎦ ⎤, B = [157]$

Text solutionVerified

Practice questions from similar books

For the matrices A and B, verify that (AB) ′ =B′ A′ where(i) A=⎣⎡​1−43​⎦⎤​,B=[−1​2​1​] (ii) A=⎣⎡​012​⎦⎤​,B=[1​5​7​]

Text solutionVerified

Practice questions from similar books

For the matrices $A$ and $B$ , verify that $(A B)^{'} = B^{'} A^{'}$ where
(i) $A = ⎣ ⎡ 1 - 4 3 ⎦ ⎤, B = [- 1 21]$
(ii) $A = ⎣ ⎡ 012 ⎦ ⎤, B = [157]$