Question: Problem 1. (4 pts) Let V and W be two vector spaces. Let T : V -> W be a linear transformation from V to

Problem 1. (4 pts) Let V and W be two vector spaces. Let T : V -> W be a linear transformation from V to W. (a) If {vi, v2. ....vx} is linearly dependent in V, prove that {T(v1). T(v2). ....(vx)} is linearly dependent in W. (b) Suppose the linear transformation T is one-to-one. If {w1, w2, . .., w} is linearly inde- pendent in V, prove that {T(w1), T(w2). ....T(wp)} is linearly independent in W

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