(P1) Let T : V W be a linear transformation of vector spaces.. Suppose the kernel of T is {0}. Show that {W1, ..., Wp} is a linearly independent subset of V if and only if {T(w),...,T(W)} is a linearly independent subset of W. (P2) Let V be the vector space of discrete time signals S. (a) Let H be the subset of S consisting of discrete time signals {f} such that fk = 0 for all k{0}. Show that H is a subspace of S. (b) Prove that H is one dimensional.