I am preparing to take an exam on Linear Algebra.
I found this question on previous exams.
Here is what I think is needed to be done.
1)First find the eigenvalues, I get:
2)There are exactly three eigenvalues, thus there are exactly three linearly independant eigenvectors. Since the eigenvectors are a subspace of the nullspace of which is of dimension three it tells us that there is basis for the eigenspace.
3)To find the basis for the eigenspace I need to substitute the eigenvalues and solve the homogenous system . Thus I need to,
Solve it by Gaussian elimination for each eigenvalue .
4)Then the basis I get for the eigenspace in #3 will be the diagnolizable matrix for by making the vectors as coloum vectors.
Is this approach correct?
I have a second question, how is "Eigenvalue" pronounced.
(At least it is not as bad, Lebesque. I never would have guess it, unless I heard someone pronouce it).