Let the matrix below act on ℂ2. Find the eigenvalues and a basis for each eigenspace in ℂ2. Let the matrix below act on C2. Find the eigenvalues and a basis for each eigenspace in C2.- 72 121areThe eigenvalues of- 72 12(Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)Find a basis for the eigenspace corresponding to the eigenvalue a + bi. Choose the correct answer below.1OA.В.6+ i11c.6+6 i6 i6 iO F.[*)6+6iOE.1Find a basis for the eigenspace corresponding to the eigenvalue a - bi. Choose the correct answer below.1OA.В.- 6i6 -[*][*)6-6.1c.16-6i6 i6 -OE.OF.11

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Answered: Let the matrix below act on ℂ2. Find…

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Let the matrix below act on ℂ2. Find the eigenvalues and a basis for each eigenspace in ℂ2.

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 24EQ

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Question

Let the matrix below act on ℂ². Find the eigenvalues and a basis for each eigenspace in ℂ².

Let the matrix below act on C2. Find the eigenvalues and a basis for each eigenspace in C2.
- 72 12
1
are
The eigenvalues of
- 72 12
(Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
Find a basis for the eigenspace corresponding to the eigenvalue a + bi. Choose the correct answer below.
1
OA.
В.
6+ i
1
1
c.
6+6 i
6 i
6 i
O F.
[*)
6+6i
OE.
1
Find a basis for the eigenspace corresponding to the eigenvalue a - bi. Choose the correct answer below.
1
OA.
В.
- 6i
6 -
[*]
[*)
6-6.
1
c.
1
6-6i
6 i
6 -
OE.
OF.
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1

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