Originally Posted by
skittle I need to determine whether U is a subspace of V. If it is not a subspace, I need to state a condition that fails and give a counter example showing that that condition fails.
a) V is the space of all differentiable functions R->R , and U is the set of differentiable functions whose derivative at 0 takes the value 1.
b) V is the space of all polynomials with real coefficients, viewed as functions R->R, and U is the set of all differentiable functions R->R.
c) V=R^4, and U= {(a, ab, b, c) belonging to R^4, a,b,c belong to R}
I know to prove that these are subspaces of V I need to prove that it is closed under scalar multiplication and addition, but I'm not sure how to write them out.