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November 23rd, 2012, 03:12 AM   #1
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NEED MATRICES (EIGENVALUE HELP) ASAP

Hi,
Okay I have absolutely no idea what to do here so i need your help asap! Ive been given homework with a deadline on matrices (I can try to hand in a day late) I honestly have no idea how to do it.

I have attatched it to this post in pdf.

If you can show me how to do these questions I would really appreciate it.

Possibly if u can also take a screenshot or photo of the steps you took to work them out. That would be awesome! Im really desperate.
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File Type: pdf emat.pdf (23.6 KB, 11 views)
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November 23rd, 2012, 08:15 AM   #2
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

Are you saying that you do not know what the "characteristic polynomial" of a matrix is? For this matrix, it is given by the determinant:


Can you find that determinant?
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November 23rd, 2012, 10:46 AM   #3
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

I've managed to get the first one but the rest of the questions are killing me. lol
I'm not too good at matrices because I haven't had time to really sit down and go through it so a lot of the stuff is really confusing.
I am basically blank in everything here(except number 1 by luck) so can you do and explain EVERYTHING please...

Thanks
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November 23rd, 2012, 10:48 AM   #4
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

Maybe make a youtube video even?
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November 23rd, 2012, 11:26 AM   #5
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

To find the eigenvalues, as in problem 1, solve the equation . That should be easy- you are told that -1 is an eigenvalue: . I am confused by your saying that you have no idea how to do problems 2 or 3. Do you not know what eigenvectors and eigenvalues are? The definition of "eigenvalue" and "eigenvector" is that v is an eigenvector of A with eigenvalue if and only if . Since you are told that 1 is an eigenvalue, a corresponding eigenvector must satisfy


Multiplying that out gives you three linear equations to solve for x, y, and z.
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November 25th, 2012, 02:14 PM   #6
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

Oh... I didnt know what to equate them to. is the answer -6x +2y +6z ? before the unit vector part..
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November 25th, 2012, 02:31 PM   #7
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Re: NEED MATRICES (EIGENVALUE HELP) ASAP

What about Q3?
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