Problem 1. Let A = ~ -8 2 2 4 4 -5 2 -5 2

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter4: Eigenvalues And Eigenvectors
Section4.3: Eigenvalues And Eigenvectors Of N X N Matrices
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Problem 1. Let A
=
-8 2
2 -5
2
24
4 -5
(1) Compute the characteristic polynomial of the matrix A.
(2) Find the eigenvalue of A and their multiplicities.
Define a dynamical system with bo
=
(1).
3
2 and bn+1
=
Abn, for n = 1, 2, 3, ..., with A as in Problem 1. Find a formula for bn
for each n.
Find the orthogonal projections of the bo of
onto the various eigenspaces of the matrix A of Problem 1.
Transcribed Image Text:Problem 1. Let A = -8 2 2 -5 2 24 4 -5 (1) Compute the characteristic polynomial of the matrix A. (2) Find the eigenvalue of A and their multiplicities. Define a dynamical system with bo = (1). 3 2 and bn+1 = Abn, for n = 1, 2, 3, ..., with A as in Problem 1. Find a formula for bn for each n. Find the orthogonal projections of the bo of onto the various eigenspaces of the matrix A of Problem 1.
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