1. The problem statement, all variables and given/known data Consider the linear transformation T from V = P2 to W = P2 given by T(a0 + a1t + a2t2) = (−4a0 + 2a1 + 3a2) + (2a0 + 3a1 + 3a2)t + (−2a0 + 4a1 + 3a2)t^2 Let E = (e1, e2, e3) be the ordered basis in P2 given by e1(t) = 1, e2(t) = t, e3(t) = t^2 Find the coordinate matrix [T]EE of T relative to the ordered basis E used in both V and W, that is, fill in the blanks below: (Any entry that is a fraction should be entered as a proper fraction, i.e. as either x/y or -x/y where x and y are positive integers with no factors in common.) T(e1(t)) = _e1(t) + _ e2(t) + _e3(t) T(e2(t)) = _e1(t) + _e2(t) + _e3(t) T(e3(t)) = _e1(t) + _e2(t) + _e3(t) and therefore : [T]EE = the combined matrix of the coefficients of the above three equations. Sorry for the poor formatting 2. Relevant equations No idea 3. The attempt at a solution I have no idea I have no idea how to do this, if someone can give me a step by step solution so that I can understand each step and process I would appreciate it greatly. Thanks for your help.