In the following, Mn,n(R) denotes the vector space of real

n × n matrices and, for A Ɛ Mn,n(R), A^T denotes the transpose of A.

1. For each of the following, either use the subspace test to show that the given

subset,

W, is a subspace of V or explain why the given subset is not a subspace

of V .

(a) V = M2,2(R) and W = {A **Ɛ **V | A^T = −A}.

(b) V = R^3 and W = {(2t, 3t,−5t) | t **Ɛ**R}.

Any ideas on how to start? I'm useless with Vector spaces and am trying to learn it now, but i really don't know how to solve the above. Please be of guidance and assisstance.