Mark each of the following statements true or false:
(a) If V = span(v1, . . . , vn), then every spanning set for V contains at least n vectors.
(b) If {u, v, w} is a linearly independent set of vectors, then so is {u + v, v + w, u + w}.
(c) M22 has a basis consisting of invertible matrices.
(d) M22 has a basis consisting of matrices whose trace is zero.
(e) The transformation T: Rn → R defined by T(x) = ||x|| is a linear transformation.
(f) If T: V → W is a linear transformation and dim V* dim W, then T cannot be both one-to-one and onto.
(g) If T: V → W is a linear transformation and ker(T) = V, then W = {0}.
(h) If T: M33 → P4 is a linear transformation and nullity(T) = 4, then T is onto.
(i) The vector space V = {p(x) in P4: p(l) = 0} is isomorphic to P3.
(j) If I: V → V is the identity transformation, then the matrix [I]C←B is the identity matrix for any bases B and C of V.