- #1
tomeatworld
- 51
- 0
Homework Statement
If A=[{5,3},{-2,-2}], find the eigenvectors of A. Using these eigenvectors as matrix P, find P-1 and thus prove P-1AP is diagonal.
Homework Equations
None
The Attempt at a Solution
So i can get the eigenvectors to be <3,-1> and <1,-2> corresponding to eigenvalues 4 and -1 respecitively. The problem however, is choosing which vector should be the first column of the matrix P. I used <3,-1> as the first column, and didn't find a diagonal matrix. Should I have? if not, how should I choose which is the first row? I don't mind trying one then the other while revising, but if it's three 3x3 matricies and I'm in a exam, trying all posiilities isn't really an option. How should you choose?