(a) Use the theoremin Picture 2to show that these three matrices are notsimilar to each other. Make sure to indicate which parts of that theorem you are using.T0100 Change of Basis MatrixIf V is an n-dimensional vector space and B = {V₁,..., Vn} and B'{W,,... W}Gare bases of V, then there is an n × n matrix, denoted by PB→B' such that forany v € V,More precisely,[V] B = PB→B'[V] B.B'PB+B¹ = [ {V₁]B² | ... | [V₂]Ð' ]If V = R" and B' = S = {e₁, ..., en} is the standard basis, thenPB+S = V₁ || Vn]=

In this question, we have to determine that which of the following matrices are similar : 1000 ,…

Answered: (a) Use the theorem in Picture 2 to…

(a) Use the theorem in Picture 2 to show that these three matrices are not similar to each other. Make sure to indicate which parts of that theorem you are using. 0 [][] 1 0 0 -1

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.6: Matrices

Problem 18E: Prove part b of Theorem 1.35. Theorem 1.35 Special Properties of Let be an arbitrary matrix...

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Question

(a) Use the theorem
in Picture 2
to show that these three matrices are not
similar to each other. Make sure to indicate which parts of that theorem you are using.
T
0
1
0
0

Change of Basis Matrix
If V is an n-dimensional vector space and B = {V₁,..., Vn} and B'
{W,,... W}
G
are bases of V, then there is an n × n matrix, denoted by PB→B' such that for
any v € V,
More precisely,
[V] B = PB→B'[V] B.
B'
PB+B¹ = [ {V₁]B² | ... | [V₂]Ð' ]
If V = R" and B' = S = {e₁, ..., en} is the standard basis, then
PB+S = V₁ |
| Vn
]
=

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