1. Label the following statements as true or false. In each part, V and W are nite-dimensional vector Spaces (over F), and T is a function from V to W. (a) (b) (C) (d) (e) (f) (s) (11) If T is linear, then T preserves sums and scalar products. If T(:c + y) = T(:c) + T(y), then T is linear. T is one-to-one if and only if the only vector 9: such that T(:r:) = 0 is x = 0. If T is linear, then T(0V) = 0W. If T is linear, then nullity(T) + rank(T) = dim(W). If T is linear, then T carries linearly independent subsets of V onto linearly independent subsets of W. If T, U: V > W are both linear and agree on a basis for V, then T = U. Given 331, $2 6 V and y1, 3,12 6 W, there exists a linear transforma- tion T: V > W such that T(.'L'1) = y1 and T(a?2) = y2