If all else fails (or maybe it should cross your mind as an earlier choice), resort to the definitions.
Your 3x3 matrix - A
Your eigenvalue - 3
An arbitrary column vector -
Ax = 3x
OK so on my homework it says Diagonalize the following matrix, if possible:
[3 2 -2]
[0 2 0]
[0 1 3]
I found out the eigenvalues which is 2 and 3. 3 is a repetition so that's why there's only 2.
Now I'm suppose to find the eigenvalue. But I have no clue how to find the eigenvector. I'm readingm y textbook and the only thing that happens is they give me the eigenvalue then mysteriously find the eigenvector within one step.
So I did Ax - 3x=0 and I got a row reduced 3x3 matrix with 2's as the diagonals Everything else are 0s... Is this suppose to be right?
I'm sorry, but I'm just really bad at this stuff >.>. I'm not even sure if I can pass the class.