Question: . Determine ifS = {p(x) = x3 + 2x2 + 3x, q[x) = 2x3 + 1, x) = 6x3 + 3x2 + 6x + 4,3(x)

. Determine ifS = {p(x) = x3 + 2x2 + 3x, q[x) = 2x3 + 1, x) = 6x3 + 3x2 + 6x + 4,3(x) = x3 + 2::2 + x + 1] is a basis for P3. . Find a basis for the subspace W of P3 consisting of all vectors of the form of bxz + cx + d where c = o 2d and b = 5a + 30!. What is the dimension of W? . Let W be the subspace of R4 generated (spanned) by the vectors [1, 2,5,3), [2.3.1, 4]J and (3.8,3. 5]. Find a basis and dimension of W

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