Label the following statements as true or false. (a) If V is a vector space and W i...

Label the following statements as true or false.

(a) If V is a vector space and W is a subset of V that is a vector space, then W is a subspace of V.

(b) The empty set is a subspace of every vector space.

(c) If V is a vector space other than the zero vector space, then V contains a subspace W such that W V.

(d) The intersection of any two subsets of V is a subspace of V.

(e) An n × n diagonal matrix can never have more than n nonzero entries.

(f) The trace of a square matrix is the product of its diagonal entries.

(g) Let W be the xy-plane in R3; that is, W = {(a₁, a₂, 0): a₁, a₂ R}.Then W = R².