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.
Put ...and now find A.