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If A=[ {matrix} 2 & -1 & 2 1 & 3 & -4 {matrix} ] and B=[ {ma

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If $A = [21 - 1 3 2 - 4]$ and $B = ⎣ ⎡ 1 - 3 5 - 2 04 ⎦ ⎤$ then verify that $(A B)^{'} = B^{'} A^{'}$

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Levi Discussed

A = [21 - 1 3 2 - 4]

and

B = ⎣ ⎡ 1 - 3 5 - 2 04 ⎦ ⎤

then verify that

(A B)^{'} = B^{'} A^{'}

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Text solutionVerified

Given

A = [21 - 1 3 2 - 4] B = ⎣ ⎡ 1 - 3 5 - 2 04 ⎦ ⎤

A B = [21 - 1 3 2 - 4] ⎣ ⎡ 1 - 3 5 - 2 04 ⎦ ⎤

= [2 + 3 + 10 1 - 9 - 20 - 4 + 0 + 8 - 2 + 0 - 16]

= [15 - 28 4 - 18]

(A B)^{1} = [15 - 28 4 - 18]

B^{1} = [1 - 2 - 3 0 54] A^{1} = ⎣ ⎡ 2 - 1 2 13 - 4 ⎦ ⎤

B^{1} A^{1} = [1 - 2 - 3 0 54] ⎣ ⎡ 2 - 1 2 13 - 4 ⎦ ⎤

= [2 + 3 + 10 - 4 + 0 + 8 - 1 - 9 - 20 - 2 + 0 - 16] = [15 - 28 4 - 18]

Hence verified

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Question Text	If $A = [21 - 1 3 2 - 4]$ and $B = ⎣ ⎡ 1 - 3 5 - 2 04 ⎦ ⎤$ then verify that $(A B)^{'} = B^{'} A^{'}$
Answer Type	Text solution:1
Upvotes	150