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0 -8 -4 -4 (a) The eigenvalues of A are λ = 3 and λ = -4. Find a basis for the eigenspace E3 of A associated to the eigenvalue λ = 3 and a basis of the eigenspace E-4 of A associated to the eigenvalue = -4. Let A = -4 0 1 0 0 3 3 0-4 000 BE3 A basis for the eigenspace E3 is = A basis for the eigenspace E-4 is

0 -8 -4 -4 (a) The eigenvalues of A are λ = 3 and λ = -4. Find a basis for the eigenspace E3 of A associated to the eigenvalue λ = 3 and a basis of the eigenspace E-4 of A associated to the eigenvalue = -4. Let A = -4 0 1 0 0 3 3 0-4 000 BE3 A basis for the eigenspace E3 is = A basis for the eigenspace E-4 is

Advanced Engineering Mathematics
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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A basis for the eigenspace E-4 is BE-47 (b) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of λ = 3: alg(3) = Algebraic multiplicity of λ = -4: alg(-4)= Geometric multiplicity of λ = 3: geo(3) = (Hint: compute the characteristic polynomial C₁(2) of A.) Geometric multiplicity of λ = -4: geo(-4)= (c) Is A diagonalizable? (No answer given) (Make sure you know how to justify your answer.)
Transcribed Image Text:A basis for the eigenspace E-4 is BE-47 (b) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of λ = 3: alg(3) = Algebraic multiplicity of λ = -4: alg(-4)= Geometric multiplicity of λ = 3: geo(3) = (Hint: compute the characteristic polynomial C₁(2) of A.) Geometric multiplicity of λ = -4: geo(-4)= (c) Is A diagonalizable? (No answer given) (Make sure you know how to justify your answer.)
Let A = -4 0 1 0 0 3 3 0-4 000 0 -8 -4 -4 (a) The eigenvalues of A are λ = 3 and λ = -4. Find a basis for the eigenspace E3 of A associated to the eigenvalue λ = 3 and a basis of the eigenspace E-4 of A associated to the eigenvalue = -4. A basis for the eigenspace E3 is 40 BE3 = A basis for the eigenspace E-4 is
Transcribed Image Text:Let A = -4 0 1 0 0 3 3 0-4 000 0 -8 -4 -4 (a) The eigenvalues of A are λ = 3 and λ = -4. Find a basis for the eigenspace E3 of A associated to the eigenvalue λ = 3 and a basis of the eigenspace E-4 of A associated to the eigenvalue = -4. A basis for the eigenspace E3 is 40 BE3 = A basis for the eigenspace E-4 is
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