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3 1 -2 4 -8 Let A = 3 -5 0 0 The eigenvalues of A are A = -2 and A= 3. Find a basis for the eigenspace E , of A associated to the eigenvalue A = -2 and a basis of the eigenspace E, of A associated (a) (: eigenvalue A = 3. A basis for the eigenspace E 2 is A basis for the eigenspace E, is HEE] BEs = (b) - ) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of A =-2 alg(-2) =| Geometric multiplicity of A = -2 geo(-2) = Algebraic multiplicity of A = 3: alg(3) Geometric multiplicity of A = 3: geo(3) (Hint: compute the characteristic polynomial CA(A) of A.) is A diagonalizable? (No answer given)

3 1 -2 4 -8 Let A = 3 -5 0 0 The eigenvalues of A are A = -2 and A= 3. Find a basis for the eigenspace E , of A associated to the eigenvalue A = -2 and a basis of the eigenspace E, of A associated (a) (: eigenvalue A = 3. A basis for the eigenspace E 2 is A basis for the eigenspace E, is HEE] BEs = (b) - ) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of A =-2 alg(-2) =| Geometric multiplicity of A = -2 geo(-2) = Algebraic multiplicity of A = 3: alg(3) Geometric multiplicity of A = 3: geo(3) (Hint: compute the characteristic polynomial CA(A) of A.) is A diagonalizable? (No answer given)

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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-- 3 1 -2 4 -8 Let A = 3 -5 3 (а) (: The eigenyalues of A are A = -2 and A= 3. Find a basis for the eigenspace E , of A associated to the eigenyalue A = -2 and a basis of the eigenspace E, of A associated to the eigenvalue A = 3. A basis for the eigenspace E_, is Bg 3= A basis for the eigenspace E, is Be = (b) - ) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of A = -2 alg(-2) =| Geometric multiplicity of A = -2 geo(-2) = Algebralc multiplicity of A = 3: alg(3): Geometric multiplicity of A = 3: geo(3) (Hint: compute the characteristic polynomial CA(A) of A.) is A diagonalizable? (No answer given)
Transcribed Image Text:-- 3 1 -2 4 -8 Let A = 3 -5 3 (а) (: The eigenyalues of A are A = -2 and A= 3. Find a basis for the eigenspace E , of A associated to the eigenyalue A = -2 and a basis of the eigenspace E, of A associated to the eigenvalue A = 3. A basis for the eigenspace E_, is Bg 3= A basis for the eigenspace E, is Be = (b) - ) State the algebraic multiplicity and the geometric multiplicity of each eigenvalue of A. Algebraic multiplicity of A = -2 alg(-2) =| Geometric multiplicity of A = -2 geo(-2) = Algebralc multiplicity of A = 3: alg(3): Geometric multiplicity of A = 3: geo(3) (Hint: compute the characteristic polynomial CA(A) of A.) is A diagonalizable? (No answer given)
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