Let T : Rn →Rm be a linear transformation.
(a) If {v1,v2,...,vk} is a linearly dependent...
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Let T : Rn →Rm be a linear transformation.
(a) If {v1,v2,...,vk} is a linearly dependent subset of Rn,prove that {T(v1),T(v2),...,T(vk)} is a linearly dependent subsetof Rm.
(b) Suppose the kernel of T is {0}. (Recall that the kernel of alinear transformation T : Rn → Rm is the set of all x ∈ Rn suchthat T(x) = 0). If {w1,w2,...,wp} is a linearly independent subsetof Rn, then show that {T(w1),T(w2),...,T(wp)} is a linearlyindependent subset of Rm.
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