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November 23rd, 2012, 03:12 AM  #1 
Newbie Joined: Nov 2012 Posts: 5 Thanks: 0  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. 
November 23rd, 2012, 08:15 AM  #2 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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? 
November 23rd, 2012, 10:46 AM  #3 
Newbie Joined: Nov 2012 Posts: 5 Thanks: 0  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 
November 23rd, 2012, 10:48 AM  #4 
Newbie Joined: Nov 2012 Posts: 5 Thanks: 0  Re: NEED MATRICES (EIGENVALUE HELP) ASAP
Maybe make a youtube video even? 
November 23rd, 2012, 11:26 AM  #5 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  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. 
November 25th, 2012, 02:14 PM  #6 
Newbie Joined: Nov 2012 Posts: 5 Thanks: 0  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..

November 25th, 2012, 02:31 PM  #7 
Newbie Joined: Nov 2012 Posts: 5 Thanks: 0  Re: NEED MATRICES (EIGENVALUE HELP) ASAP
What about Q3?


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