Given the two matrices, A=begin{bmatrix}1 & 2&3 1 & 1&20&1&2 end{bmatrix} text{ and } B=begin{bmatrix}1 & 1&1 2 & 1&23&1&2 end{bmatrix} (a) Find det A

Cabiolab 2021-02-15 Answered

Given the two matrices,
A=[123112012] and B=[111212312]
(a) Find det A, det B , det(AB) , det(BA) , det(5A) , detAT and det(B6)
(b) Find adj A and adj B
(c) Find A1 and B1 using the adjoint matrices you found in part (b)

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Expert Answer

odgovoreh
Answered 2021-02-16 Author has 107 answers

Step 1
We have given the matrices
A=[123112012] and B=[111212312]
Step 2
Part(a)
Find det A:
detA=det[123112012]=1det[1212]2det[1202]+3det[1101]
=1022+31
=-1 Find det B:
detB=det[111212312] =1det[1212]1det[2232]+1det[2131]
=101(2)+1(1)
=1
Step 3
Find det(AB) and det(BA)
According to determinant properties,
det(AB)=detA×detB
=1×1
=-1
det(BA)=detB×detA
=1×1
=-1
Step 4
Find det(5A)
det(5A)=53×detA
=125×1
=-125
Find detAT:
detAT=detA
=-1
Find det(B6):
det(B6)=(detB)6
=16
=1
Step 5
Part (b)
Find adj A and adj B
A=[123112012]
The cofactors matrix is
C=[+det[1212]det[1202]+det[1101]det[2312]+det[1302]det[1201]+det[2312]det[1312]+det[1211]]
C=[+(22)(20)+(10)(43)+(20)(10)+(<

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Jeffrey Jordon
Answered 2022-01-27 Author has 2047 answers

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