Consider the matrices A=begin{bmatrix}1 & -1 0 & 1 end{bmatrix},B=begin{bmatrix}2 & 3 1 & 5 end{bmatrix},C=begin{bmatrix}1 & 0 0 & 8 end{bmatrix},D=be

Jaden Easton 2020-12-16 Answered
Consider the matrices
A=[1101],B=[2315],C=[1008],D=[201143542] and F=[210011203]
a) Show that A,B,C,D and F are invertible matrices.
b) Solve the following equations for the unknown matrix X.
(i) AXT=BC3
(ii) A1(XT)T=(B1)T
(iii) XF=F1DT
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Expert Answer

estenutC
Answered 2020-12-17 Author has 81 answers

Step 1
(a) A matrix S is invertible if the determinant of the matrix is not 0
That is , det(S)0
Step 2
Consider the matrix A
A=[1101]
Obtain the detrminant of A
det(A)=1(1)(1)0
=1+0
=1
0
Hence , A is invertible
Step 3
Consider the matrix B
A=[2315]
Obtain the detrminant of B
det(B)=2(5)(3)1
=103
=7
0
Hence , B is invertible
Step 4
Consider the matrix C
C=[1008]
Obtain the detrminant of A
det(C)=1(8)(0)0
=8
0
Hence , C is invertible
Step 5
Consider the matrix D
D=[201143542]
Obtain the detrminant of D
det(D)=2[812]0[215]1[420]
=2(4)(16)
=8
0
Hence , D is invertible
Step 6
Consider the matrix F
F=[210011203]
Obtain the detrminant of F
det(F)=2[30]+1[02]+0[02]
=2(3)+(2)
=62=4
0
Hence , F is invertible
Thus, A, B, C, D and F are invertible matrices.

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Jeffrey Jordon
Answered 2022-01-23 Author has 2064 answers

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