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Question: 24 please...

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24. Prove that if R R is a one-to-one lincar transformation and S - ,v ...v) is of linearly independent vectors from R, then TVi). T2 independent vectors from R. ), T(V2), ..., T(Vi) is a set of linearly Hint: Begin the proof by considering the dependence test equation: Rewrite the left side using the linearity properties of T and use the Kernel Test for Injecti vity. 25. Use the previous Exercise to prove that if T : R R is one-to-one and S-(V1,V2, 2% } is any basis for R, then TV). Th), . . . . Tv.) } is a basis for range(T). 26, Let 7, : R → Rk and T2 : Rk → Rm a. What is the ambient space of range(T1)? 24 please
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