599). . 0. Let F be a field, let f(x) = co+c++ cd-12-1+xd be a monic polynomial in F[r], and let T be the operator on Fd with matrix (with respect to the standard basis) 0 the companion matrix to f(x). 1 0 C₁ = 0 (a) Show that the minimal polynomial for T is f(x). (b) Show that XT(x)=(-1)df(x). -CO .. 0 0-cd-2 0 1 -Cd-1
599). . 0. Let F be a field, let f(x) = co+c++ cd-12-1+xd be a monic polynomial in F[r], and let T be the operator on Fd with matrix (with respect to the standard basis) 0 the companion matrix to f(x). 1 0 C₁ = 0 (a) Show that the minimal polynomial for T is f(x). (b) Show that XT(x)=(-1)df(x). -CO .. 0 0-cd-2 0 1 -Cd-1
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter7: Eigenvalues And Eigenvectors
Section7.CM: Cumulative Review
Problem 5CM: Find the kernel of the linear transformation T:R4R4, T(x1,x2,x3,x4)=(x1x2,x2x1,0,x3+x4).
Related questions
Question
1. Explain simplify
![599).
.
0. Let F be a field, let f(x) = co+c++ cd-12-1+xd be a monic polynomial in F[r], and
let T be the operator on Fd with matrix (with respect to the standard basis)
0
the companion matrix to f(x).
1
0
C₁ =
0
(a) Show that the minimal polynomial for T is f(x).
(b) Show that XT(x)=(-1)df(x).
-CO
.. 0
0-cd-2
0
1 -Cd-1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F30e6ca29-61bc-41d1-bea3-28d53872fdaf%2F84c56977-f0a0-4ddb-b3d2-0cd206c580e1%2Fmjdgele_processed.jpeg&w=3840&q=75)
Transcribed Image Text:599).
.
0. Let F be a field, let f(x) = co+c++ cd-12-1+xd be a monic polynomial in F[r], and
let T be the operator on Fd with matrix (with respect to the standard basis)
0
the companion matrix to f(x).
1
0
C₁ =
0
(a) Show that the minimal polynomial for T is f(x).
(b) Show that XT(x)=(-1)df(x).
-CO
.. 0
0-cd-2
0
1 -Cd-1
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