Eigenvalues and eigenvectors of a 3x3 matrix A? A unknown?
I need some help with the following problem please?
Let A be a 3x3 matrix with eigenvalues -1,0,1 and corresponding eigenvectors
l1l . l0l . l0l
l0l ; l1l ; l1l respectively.
l0l . l1l . l2l
I know that I need to work backwards on this problem so I set up the characteristic equation with th known eigenvalues ending up with x^3-x=0 but now I'm stuck I don't know where to go from here and how to use the eigenvectors. I can set up A with all unknowns and subtract it from kI where k is the eigenvalue and I is the identity matrix then find the determinant, but there are too many unknowns and too few equations. I'm totally confused.
Can someone please assist?
Thanks in advance.