The matrix The eigenvalue ₁ is A = The eigenvalue λ2 is 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. 2 and a basis for its associated eigenspace is and a basis for its associated eigenspace is

The matrix The eigenvalue ₁ is A = The eigenvalue λ2 is 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace. 2 and a basis for its associated eigenspace is and a basis for its associated eigenspace is

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter5: Orthogonality

Section5.3: The Gram-schmidt Process And The Qr Factorization

Problem 8BEXP

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Question

The matrix
The eigenvalue 1 is
0
A = 1
1
0
1 -1
has two real eigenvalues, one of multiplicity 1 and one of multiplicity 2. Find the eigenvalues and a basis for each eigenspace.
The eigenvalue λ2 is
-1
1
2
and a basis for its associated eigenspace is
{
and a basis for its associated eigenspace is

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Step 1: Introduction

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Step 2: Find the eigenvalues of the given matrix A

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Step 3: Find the basis for the eigenspace associated to eigenvalue λ=0

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Step 4: Find the basis for the eigenspace associated to eigenvalue λ=1

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