Question: Let T : V - W be a linear transformation, and suppose the nullspace of T is {0}. Let S = {X1, X2, ..., Xk}

Let T : V - W be a linear transformation, and suppose the nullspace of T is {0}. Let S = {X1, X2, ..., Xk} be a linearly independent subset of V. Show T(S) = {T(X1 ), T( X2 ) , . .., T(Xk) } is a linearly independent subset of W

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