I have reduced a matrix to the following:
Obviously .
How do I figure out what is here?
I did this a few years ago but am lost right now... I have the answer for this problem but I don't understand how to reach it myself.
Cheers to anybody interested!
What FernandoRevilla told you was that the general solution to your original problem is of the form . That can be written as . The two eigenvectors are and . A three by three matrix may have up to three independent eigenvectors- whether that is true in this case depends upon the original matrix. What did you get for the eigenvalues?
What are you given as the definition of "eigenvector"?
Sorry for late response - and thanks for adding a reply.
The question I was trying to get my head around was this:
Find eigenvalues and eigenvectors of
To which I found .
Then, for
So, and I am trying to remember here (!), we describe the vector x in terms of parameters. Which I should have done as
(is this right ?!)
That's right.
Note that the vector x represents an eigenvector (for eigenvalue 3).
So any eigenvector (with eigenvalue 3) can be expressed as a linear combination of (1,1,0) and (0,0,1) and in particular two linearly independent eigenvectors will be (1,1,0) and (0,0,1) (and any scalar multiplies of these two vectors!)