{:09K/s4 583944816...->MATH 107Assignment # 3Linear Algebra1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.(b)(a)4-2 1-2 0 1.[4 0(d) o 3li o(e)2. Find a 3 x 3 matrix A that has eigenvalues 1, -1, and 0, and for whichE BEL.are their corresponding eigenvectors.3. Find a matrix P that diagonalizes A and check your work by computing P-'AP.(a) A =-2(b) A = 0 3104. Let[1 -4and P =1-2A =Confirm that P diagonalizes A, and then compute each of the following powers of A.(а) А1000() А-1000 (с) А2301 (d) А-23015.Find the basis for the eigenspace corresponding to the given eigenvalues,(a)(b)-41, 3A =A=-5-333-2

"Since you have asked multiple questions with multisubparts, we will solve the first question with…

Answered: 1. Find the characteristic equation,…

1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix. (b) [2] (a) 1 40 (c) -2 1 -20 [4 (d) 0 3 0 0 -1] 2

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter4: Eigenvalues And Eigenvectors

Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices

Problem 41EQ

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Question

{:09
K/s
4 583944816...
->
MATH 107
Assignment # 3
Linear Algebra
1. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.
(b)
(a)
4
-2 1
-2 0 1.
[4 0
(d) o 3
li o
(e)
2. Find a 3 x 3 matrix A that has eigenvalues 1, -1, and 0, and for which
E BEL.
are their corresponding eigenvectors.
3. Find a matrix P that diagonalizes A and check your work by computing P-'AP.
(a) A =
-2
(b) A = 0 3
10
4. Let
[1 -4
and P =1
-2
A =
Confirm that P diagonalizes A, and then compute each of the following powers of A.
(а) А1000
() А-1000 (с) А2301 (d) А-2301
5.
Find the basis for the eigenspace corresponding to the given eigenvalues,
(a)
(b)
-4
1, 3
A =
A=-5
-3
3
3
-2

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