Find Eigenvectors in a 3x3-matrix
I'm having trouble with finding the eigenvectors of a 3x3 matrix. The matrix M, is defined as the following:
|0 ||0.3 ||0.4 |
|0.6 ||0 ||0.6 |
|0.4 ||0.7 ||0 |
Having found det(M - ÆI), where ÆI is matrix:
I have found the following eigenvalues:
I am now to find the corresponding eigenvectors, V1, V2, V3, but I can't seem to approach it the right way. I have the following system of equations:
For Æ1 = 1:
| ||0.3y + ||0.4z ||= ||x |
|0.6x + || ||0.6z ||= ||y |
|0.4x + ||0.7y || ||= ||z |
And similarly for the remaining eigenvalues.
How do I go about finding the eigenvectors? ANY help is highly appreciated!
Re: Find Eigenvectors in a 3x3-matrix
Given the eigenvalues of a matrix, (by definition) to find the corresponding eigenvectors, solve the following system:
So, for the first eigenvalue, λ = 1, the system would become as follows:
Solve this equation.
Then repeat this process for the other two eigenvalues to find the corresponding eigenvectors.