Determine which of the following is a subspace of the appropriate vector space.

If it is a subspace, prove that it is. If it is not a subspace, give an example to show why it is not a subspace.

a) The set of 2 £ 2 matrices A so that Av = 0 for the vector

~v = 1

1

b) The set of 2 £ 2 matrices A so that A2v = 0 for the vector

~v = 1

1

c) The set of polynomials p(x) 2 P so that p(3) = p(1) = 0.

c) The set of polynomials p(x) 2 P so that p(3) = p(1) = 1.