H6 part b
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Linear Transformations
Section6.CR: Review Exercises
Problem 29CR: Use the standard matrix for counterclockwise rotation in R2 to rotate the triangle with vertices...
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H6 part b
![Log In
Sep
12
Read your lecture notes and do
Sec 2.3: 1 and
watch the 61-minute video on companion matrices and rational canonical form (use the link
provided or access it in the Modules section of our Canvas portal) and then do
H4. (a) Compute the companion matrix for the polynomial found in Question 2.3.1.
(b) Compute the companion matrix of the characteristic polynomial of the matrix given in
Question 2.1.11.
H5. (a) Suppose A and B are similar matrices. Show that AK = 0 iff Bk = 0, where k € N.
(b) Find the characteristic polynomial of the matrix A4 given in H1.
(c) Compute the companion matrix C of the polynomial found in (b).
(d) Compute A4² and C².
(e) Use (a) and (d) to show that A4 and C are NOT similar matrices.
(H5(e) motivates using rational canonical form instead of C.)
H6. Find the rational canonical form of each of the following matrices:
(a) the matrix A4 given in H1
[200]
(b) 0 2 0
0 02
[2 1 01](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc074fc7e-4e48-46f1-bfc4-aee6ba4e6262%2Fcbd74f6d-a034-419d-8e09-f01462172fc5%2Fa2p5l7g_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Log In
Sep
12
Read your lecture notes and do
Sec 2.3: 1 and
watch the 61-minute video on companion matrices and rational canonical form (use the link
provided or access it in the Modules section of our Canvas portal) and then do
H4. (a) Compute the companion matrix for the polynomial found in Question 2.3.1.
(b) Compute the companion matrix of the characteristic polynomial of the matrix given in
Question 2.1.11.
H5. (a) Suppose A and B are similar matrices. Show that AK = 0 iff Bk = 0, where k € N.
(b) Find the characteristic polynomial of the matrix A4 given in H1.
(c) Compute the companion matrix C of the polynomial found in (b).
(d) Compute A4² and C².
(e) Use (a) and (d) to show that A4 and C are NOT similar matrices.
(H5(e) motivates using rational canonical form instead of C.)
H6. Find the rational canonical form of each of the following matrices:
(a) the matrix A4 given in H1
[200]
(b) 0 2 0
0 02
[2 1 01
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