Linearly Independent Vectors and Invertible Matrices
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If you let {v1, v2,...,vk} be linearly independent vectors in and A & B are n x n matrices. If you assume A is invertible how would you show that {A(v1), A(v2,)...,A(vk)} are linearly independent?
Also, if you know that {v1, v2,...,vk} are linearly independent and {B(v1), B(v2,)...,B(vk)} are linearly independent, how do you prove that B is invertible?
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Linearly Independent Vectors and Invertible Matrices are investigated. The solution is detailed and well presented. The response was given a rating of "5/5" by the student who originally posted the question.
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Proof:
Since are linearly independent, then we have
(a) For invertible matrix and the set of vectors ...
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