Hi,

Thank you so much for the help before. I appreciate it.

I have 2 new problems to solve. Please, help me!

1. Prove or disprove if U, V, W are subspaces of V for which

U (dir sum) W = V (dir sum) W then U=V

2. Suppose that p_0,...p_3 are polynomials in the space P_m(F) (of polynomials over F with degree at most m) such that p_j(2)=0 for eachj. Prove that the set {p_0,...,p_m} is not lin. independant in P_m(F).

Thank you in advance!