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.