Compute the dimension and find bases for the following linear spaces.

a) Real anti-symmetric 4 × 4 matrices.
b) Quartic polynomials p with the property that p(2) = 0 and p(3) = 0.
c) Cubic polynomials p(x, y) in two real variables with the properties: p(0, 0) = 0,
p(1, 0) = 0 and p(0, 1) = 0.
d) The space of linear maps L : R5 ? R3 whose kernels contain (0, 2,-3, 0, 1).