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
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Chapter2: Second-order Linear Odes
Section: Chapter Questions
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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.
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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