Question

Linear Algebra Question:

4. True or False. Justify carefully your answer.
(a) The set S of all polynomials of the form p(t) = 1 + at + bt^2 with a and b in R is a subspace of P2(R).
(b) The set H of all vectors in R3 whose last entry is zero is a subspace of R3.
(c) If A is a 5 x 7 matrix of Rank 3, then Nul(A) is a subspace of dimension 4.