2 -2 1) Find the eigenvalues and eigenvectors of the matrix B = -1 1 -2 1 -1

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.1: Inner Product Spaces
Problem 10AEXP
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Question
2
-
1) Find the eigenvalues and eigenvectors of the matrix B = -1
1
- 2
1
-1
2) Given B = {B,, B2, ß3} where Bi
B2
=|0, B3 =
- 3
%3D
1
i) Show that B is a basis for R³.
ii) Determine an orthonormal basis of R based on B.
Transcribed Image Text:2 - 1) Find the eigenvalues and eigenvectors of the matrix B = -1 1 - 2 1 -1 2) Given B = {B,, B2, ß3} where Bi B2 =|0, B3 = - 3 %3D 1 i) Show that B is a basis for R³. ii) Determine an orthonormal basis of R based on B.
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