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=Rhea Section for MA 35100 Professor Kummini, Spring 2011=
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Can anyone please help me in the question no. 25 of exercise 7.3? I am having a lot of trouble in comprehending how to calculate the multiplicity.
  
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The geometric multiplicity of a matrix is directly related to the no. of independent eigenvectors in the eigen basis. Since, the no. of independent vectors is 3 (column wise), therefore, the geometric multiplicity is 3.
  
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Can anyone please explain me how to go about solving Q. 14 Exercise 7.3 ? i guess i'm probably making a mistake somewhere in my calculations ...  
  
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Hello, I am getting the lambda values to be 0,0,1 for the question. The determinant value becomes 0 =-(lambda)^3+ 2(labmda)^2 - labmda.Now it should be pretty straight forward to find out the corresponding eigen-vectors.
==Discussions==
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*[[How_to_evaluate_this_sum_ECE301S11|Can you help an ECE student evaluate a complicated sum?]]
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Hi, for Q. 14 in Section 7.3, I calculated the determinant to be 0 = [-(lambda)][(1-lambda)^2].  Therefore, I got three eigenvalues of: lambda = 0, lambda = 1, lambda = 1.  Which led to an eigenbasis of: [0 1 0], [1 -5 0], [0 2 1]. 
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[[Category:MA35100Spring2011Kummini]]
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<br> Hey friends, like geometric multiplicity of an eigenvalue is related to the nullity of the matrix (A- λIn), is there a way to relate algebraic multiplicity on similar terms&nbsp;?  
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Yea.I meant orthogonal.sorry. Thank you though for the answer.
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<br> Review for final Chapter 1 &amp;2 by B Zhou [https://kiwi.ecn.purdue.edu/rhea/index.php/Homework_MA351_Spring_2011]  
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Review for final Chapter 3&amp;4 By B zhou [https://kiwi.ecn.purdue.edu/rhea/index.php/Chpater3%264_MA351Spring2011]  
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Various exercises from Chapters 6 &amp; 7, by Dan Coroian (dcoroian)&nbsp;[[Final review Chs. 6 & 7 (MA351Spring2011)|Final review]]  
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Hey.Can anyone please explain me the 20th question of exercise 7.1. I am not able to understand how to interpret the question. Thanks
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I believe that there would be no eigenvalue corresponding to the rotation in about e3 in R3&nbsp;! However, I would recommend asking the question to Prof. Kummini in this regard&nbsp;!
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Hey I think the eigenvalue would be 1 since any vector on the axis spanned by e3 would be an eigen vector&nbsp;!
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I'm having some trouble calculating Q. 14 of Section 7.1.  If someone is able to start it out I would really appreciate it!

Latest revision as of 12:27, 6 May 2011

Can anyone please help me in the question no. 25 of exercise 7.3? I am having a lot of trouble in comprehending how to calculate the multiplicity.

The geometric multiplicity of a matrix is directly related to the no. of independent eigenvectors in the eigen basis. Since, the no. of independent vectors is 3 (column wise), therefore, the geometric multiplicity is 3.

Can anyone please explain me how to go about solving Q. 14 Exercise 7.3 ? i guess i'm probably making a mistake somewhere in my calculations ...

Hello, I am getting the lambda values to be 0,0,1 for the question. The determinant value becomes 0 =-(lambda)^3+ 2(labmda)^2 - labmda.Now it should be pretty straight forward to find out the corresponding eigen-vectors.

Hi, for Q. 14 in Section 7.3, I calculated the determinant to be 0 = [-(lambda)][(1-lambda)^2]. Therefore, I got three eigenvalues of: lambda = 0, lambda = 1, lambda = 1. Which led to an eigenbasis of: [0 1 0], [1 -5 0], [0 2 1].


Hey friends, like geometric multiplicity of an eigenvalue is related to the nullity of the matrix (A- λIn), is there a way to relate algebraic multiplicity on similar terms ?

Yea.I meant orthogonal.sorry. Thank you though for the answer.




Review for final Chapter 1 &2 by B Zhou [1]


Review for final Chapter 3&4 By B zhou [2]


Various exercises from Chapters 6 & 7, by Dan Coroian (dcoroian) Final review


Hey.Can anyone please explain me the 20th question of exercise 7.1. I am not able to understand how to interpret the question. Thanks

I believe that there would be no eigenvalue corresponding to the rotation in about e3 in R3 ! However, I would recommend asking the question to Prof. Kummini in this regard !

Hey I think the eigenvalue would be 1 since any vector on the axis spanned by e3 would be an eigen vector !


I'm having some trouble calculating Q. 14 of Section 7.1. If someone is able to start it out I would really appreciate it!

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