Well, you evaluate that determinant now! That will, of course, depend on . In fact, it will be a cubic equation.
Expanding on the top row, that is equal to
Multiply that out and solve for .
I am trying to work out some Matrix questions in advance to my course start.
I am trying to find the eigenvalues for this 3 x 3 Matrix:
5 3 2
1 4 6
9 7 3
So far I have got to:
5-L ... 3 ... 2
1 ... 4-L ... 6
9 ... 7 ... 3-L
I am not sure where to go next - Can anybody help?
I checked with MatLab and an online cubic calculator and got -2.568, 1.659, 12.909 as my eigenvalues, so that's all good.
How do I go about finding the Eigenvectors for these eigenvalues?
Any help is greatly appreciated.
The eigenvector corresponding to a certain eigenvalue is the vector x such that .
Lambda is one of the three eigenvalues.
There are thus 3 eigenvectors in this problem.
Using Matlab you can find the eigenvectors using: where V are the vectors (1 column is 1 vector), L are the eigenvalues (lambdas) and M is your input matrix.
The eigenvector corresponding to the eigenvalue, 12.9094 is .
I hope this helps...