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

Jaden Easton

Answered question

2020-12-16

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

Answer & Explanation

estenutC

estenutC

Skilled2020-12-17Added 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.

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-23Added 2605 answers

Answer is given below (on video)

Jeffrey Jordon

Jeffrey Jordon

Expert2022-08-23Added 2605 answers

Answer is given below (on video)

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?