questions:

.. (a) Which of the subsets U1 = {PEP(R) : p(0) = 0} , U2 = {PEP(R) : P(0) = 1} , U3 = {PEP(R) : p(1) = 0} , UA = PEP(R) : / p(x) d.x = 0 o Us = {PEP(R) : p'(0) + p"(0) = 0} , U6 = {PEP(R) : p'(0)p"(0) = 0} of P(R) are subspaces of P(R)? b) Which of the subsets of R2x2 are subspaces of R2x2