Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C². 45 -54 45 The eigenvalues of -54 (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) are A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is (Type an exact answer, using radicals and i as needed.) A basis for the eigenspace corresponding to the eigenvalue a - bi where b>0, is (Type an exact answer, using radicals and i as needed.)
Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C². 45 -54 45 The eigenvalues of -54 (Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.) are A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is (Type an exact answer, using radicals and i as needed.) A basis for the eigenspace corresponding to the eigenvalue a - bi where b>0, is (Type an exact answer, using radicals and i as needed.)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².
4 5
- 5 4
45
- 5 4
(Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
The eigenvalues of
are
A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is
(Type an exact answer, using radicals and i as needed.)
A basis for the eigenspace corresponding to the eigenvalue a - bi where b>0, is
(Type an exact answer, using radicals and i as needed.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fbe763e4e-f795-40b2-8fd9-57a3e5a9095e%2Fdc6c2315-b98e-42cc-bc62-4249bd6bbd84%2Fobx5sy3_processed.png&w=3840&q=75)
Transcribed Image Text:Let the matrix below act on C². Find the eigenvalues and a basis for each eigenspace in C².
4 5
- 5 4
45
- 5 4
(Type an exact answer, using radicals and i as needed. Use a comma to separate answers as needed.)
The eigenvalues of
are
A basis for the eigenspace corresponding to the eigenvalue a + bi, where b>0, is
(Type an exact answer, using radicals and i as needed.)
A basis for the eigenspace corresponding to the eigenvalue a - bi where b>0, is
(Type an exact answer, using radicals and i as needed.)
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