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Eigenvalues - Linear Algebra - Quiz Solution, Exercises of Linear Algebra

This is the Quiz Solution of Linear Algebra. Mainly includes points are Explicit Conditionsm, Expansion Across, Equilibrium Prices, Equation, Elementary, Elementary Row etc. Key important points of tags are: Eigenvalues, Values, Multiplicity, Real Eigenvalues, Three Facts, Eigenvector, Vector, Question, Eigenspace, Characteristic Polynomial

Typology: Exercises

2012/2013

Uploaded on 02/27/2013

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Math 205B Quiz 07 page 1 03/12/2010 Name. Susgasied salhion 1. Suppose that =| 9, oF 1A. Find all values of k for which M has \ = 3 as an eigenvalue with multiplicity 2. Show all your work. =e a a = (o-r)(6-»)tK = \- 6d 4K a 2 HERE we reguive. \*-6rX +k = (-3) » 1B. Find all values of k for which M has eigenvalues 5 and 1. Show all your work. Mo ue feguine Hat '-Gd+K = O-H>-9, tach 6 N-EN*S 1C. Find all values of k for which M has no real eigenvalues. Show all your work. th rob f N=G>*K in general aoe + /%-4K z= Get ay qt at. ea > 36-K< O S %< MK 2 8 -3 2 2.LetA=| 2 1 4 |. Here are three facts about A: Fact 1) One eigenvalue of A is a = 7. -5 15 -3 1 Fact 2) The vector v= | 2 | is an eigenvector of A for some other eigenvalue 6 # 7. —5 Fact 3) In no part of this question do you need to use determinants. 2A. Use fack 2 to find that other eigenvalue 8. Show all your work. ( -§ ( A |= “he --«(s]>@-9) s ce) 2B. Find a basis for the eigenspace for the eigenvalue 7. Show all your work. pref (A-72) = ref E 7 ‘); fe | > a 7 tes HE (3 basis 0 bedter) 2C. Find the characteristic polynomial of A. pote vel, SCE. te ign 4 a ie 2, fhe mabey of ? = ee fan (>=?) ml (48) rat ton 6 hor 4 cher spa 4p ol Ae IBD digree of “4 dhe pay 6 3. THE Uy porsboily 5 i (- Aang (2% pethops be Ke Li = )