Difference between revisions of "2011 Spring MA 35100 Kummini" - Rhea

Revision as of 09:23, 5 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.

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 Final Review Chs. 6 & 7 (MA351Spring2011)

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 !