Let V and W be vector spaces and let T E L(V, W). (a) Suppose V is finite-dimesnional, m is a finite positive integer, and wi, ..., wm is a basis for range T. Show that there exist vectors v; E V, 1 < i< m, such that Tv; = w;, and show that these vectors v; are independent. Also show that span(v1,..., vm) null T = V.

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A: Given V is a n- dimensional vector space. Let B be a basis for V. Let B=v1, v2, …, vn. Let u1, u2,…

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