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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.
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
Solve.
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.