1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue. 2 01 A -1 -1 1 0 1 = [0], v₂ = [1], v₁ = [1] corresponding to eigenvalues 2. A is a 3 x 3 matrix with eigenvectors v₁ = 0,0₂ V3
1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue. 2 01 A -1 -1 1 0 1 = [0], v₂ = [1], v₁ = [1] corresponding to eigenvalues 2. A is a 3 x 3 matrix with eigenvectors v₁ = 0,0₂ V3
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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Question
![1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each
eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue.
1
2
01
A =|-1
-1
1
1
1.
2. A is a 3 × 3 matrix with eigenvectors vị = |0|,v2 =
,V3 =
corresponding to eigenvalues
21 = -12 =z = 1, respectively, and x = |1|. Find A2ºx.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8dc5f49c-87a9-4153-93d3-b3c8983090ac%2F33c7e60c-03f8-4632-af22-a89f0034177e%2Fzo7zyar_processed.jpeg&w=3840&q=75)
Transcribed Image Text:1. Compute (a) the characteristic polynomial of A, (b) the eigenvalues of A, (c) a basis for each
eigenspace of A, and (d) the algebraic and geometric multiplicity of each eigenvalue.
1
2
01
A =|-1
-1
1
1
1.
2. A is a 3 × 3 matrix with eigenvectors vị = |0|,v2 =
,V3 =
corresponding to eigenvalues
21 = -12 =z = 1, respectively, and x = |1|. Find A2ºx.
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