1. The problem statement, all variables and given/known data Let T:P2→P2 be defined by T(a0+a1x+a2x2)=(2a0-a1+3a2)+(4a0-5a1)x + (a1+2a2)x2 1) Find the eigenvalues of T 2) Find the bases for the eigenspaces of T. I believe the 'a' values are constants. 2. Relevant equations None. 3. The attempt at a solution The problem I am having is actually pulling out the matrix for T. I know how to find eigenvalues (by solving det(λI-A) - A being the matrix) and from that finding the bases of the eigenspaces comes from substituting the eigenvalues into (λI-A) and performing elementary row operations to find the eigenvectors which form the bases. What I have tried to do is separate the basis (1,x,x2) from the rest and come up with the matrix : 2a0 -a1 3a2 4a0 -5a1 0a2 0a0 a1 2a2 Am I on the right track here or am I barking up the wrong tree? If so what method should i follow?