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Please answer the given question in detail: Prove that every linearly independent subset of vectors in Rm is part of a basis. So, given a

Please answer the given question in detail:

Prove that every linearly independent subset of vectors in Rm is part of a basis. So, given a linearly independent subset of vectors (say k of them) in Rm, we can always find m - k vectors to extend the inital subset to a basis for Rm

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