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Proof in numerical linear algebra explained in this solution

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Suppose that C [an element of] C^nxn is invertible and the set S = {w_1,...w_k} C [a subset of] C^n is linearly
independent. Prove that CS := {Cw_1,...Cw_k} C [a subset of] C^n is linearly independent.

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Proof in numerical linear algebra is clearly demonstrated in this solution.

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