►(a)(b)(c)(f)(g)Consider the following matrices-3 40A-2 30-88 1(i)0170 -1191.00 0Find the characteristic polynomial of matrix A."and B and vector b,G03B =Find eigenvalues of the matrix A.(d)What is the algebraic and geometric multiplicities of the eigenvalues of A.(e)Show that the matrix A is diagonalizable and find an invertible matrix P anda diagonal matrix D such that P-¹AP = Db=Find a basis for the eigenspaces of matrix A.Find A¹0b by writing b as linear combination of eigenvectors of A.Find a formula for Ak for all non-negative integers k.Use (g) to find A¹0b and compare it with what you found in (VI).Is A similar to B? If yes, find an invertible matrix such that P-¹AP = B.

Answered: Image /qna-images/answer/b69c8e5d-9960-437a-8253-566573909936.jpg

E (a) (b) (c) Consider the following matrices -3 4 07 A-2 30 -8 8 1 and B and vector b, H 0 3 1 0 1] B 0 -1 0 0 0 1 Find the characteristic polynomial of matrix A. " Find eigenvalues of the matrix A. b= Find a basis for the eigenspaces of matrix A.

E (a) (b) (c) Consider the following matrices -3 4 07 A-2 30 -8 8 1 and B and vector b, H 0 3 1 0 1] B 0 -1 0 0 0 1 Find the characteristic polynomial of matrix A. " Find eigenvalues of the matrix A. b= Find a basis for the eigenspaces of matrix A.

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Question

►
(a)
(b)
(c)
(f)
(g)
Consider the following matrices
-3 4
0
A-2 30
-88 1
(i)
0
17
0 -1
191.
0
0 0
Find the characteristic polynomial of matrix A.
"
and B and vector b,
G
0
3
B =
Find eigenvalues of the matrix A.
(d)
What is the algebraic and geometric multiplicities of the eigenvalues of A.
(e)
Show that the matrix A is diagonalizable and find an invertible matrix P and
a diagonal matrix D such that P-¹AP = D
b=
Find a basis for the eigenspaces of matrix A.
Find A¹0b by writing b as linear combination of eigenvectors of A.
Find a formula for Ak for all non-negative integers k.
Use (g) to find A¹0b and compare it with what you found in (VI).
Is A similar to B? If yes, find an invertible matrix such that P-¹AP = B.

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