consider the matrix A

Question

Consider the matrix A = [  1  3  0]

                                    [3    1  0]

                                   [0   0  -2]

 

 

(a) find the eigenvalues for A

(b) Find a matrix P such that P-1AP is a diagonal matrix

(c) is it possible to find an orthogonal matrix P such that P-1AP is a diagonal matrix? if so, find P.

 

can you please also show me all the steps 

Answer 1

Sammy,

 

(a) To find the eigenvalues for A, you must solve the equation det(A - λI) = 0, where I is the 3x3 identity matrix.

(b) In order to solve this question, you must also find the eigenvectors and verify that they are linearly independent. Can you do this?

(c) Once you find the linearly independent eigenvectors, you can apply the Gram-Schmidt process to orthonormalize them. You can then construct the transition matrix P as required.

 

This is much too long a problem for any tutor to expend time sending you a lengthy solution. I recommend you try my hints and then post replies as needed. Also, the procedures for doing these three questions should be written in your textbook. If you are having trouble understanding the steps, you can ask more specific questions or consult with your instructor.

 

Sorry I cannot be of more help, but this will at least get you started. Don't take it personally.