1. The problem statement, all variables and given/known data T: R3[x] R3[x] // for some reason the arrow symbol isn't working! When I do the arrow it previews as the third power for some reason. Also, whenever I preview post, it adds 1 2 b again for some reason and I have to delete those lines every time...a bit fustrating... T(1) = 3 + 2x +4X2 T(x) = 2 + 2x2 T(x2) = 4 + 2x 3x2 Find all eigenvalues and their linear subspaces they create. 3. The attempt at a solution I don't exactly understand what to do here. I am used to transformations from R3 to R3, not the polynomial transformations. And I am a bit confused how they wrote T(1) T(x) and T(x2) separately. Is that the way you write the transformations for polynomials? I thought it should be like this: T(alpha0 + alpha1x + alpha2x2) = (.....) I guess I just need someone to explain what T(1) = 3 + 2x +4X2 T(x) = 2 + 2x2 T(x2) = 4 + 2x 3x2 means. Thanks.