Use the subspace test to show whether or not W is a subspace of V:

1) V = R^3 and W = {7t, -3t, t x sqrt(5) | t E R}

2) V = R^3 and W = {x,y,z E V | xy + yz + xz = 0}

3) V = P2(R) (real polynomial functions of degree at most 2) and W = {f E V | f(1) = f(-1)}

Hi,

These are the problems presented. Now I have a clear idea of what the subspace test is and the conditions that must be met but I don't know what to do. Now this is a big step up from what I have been doing and the new material has somewhat phased me so please someone help me with a way into this. For a start what is R^3?