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Thread: [Linear Algebra] Determine if a set is a basis

  1. #1
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    [Linear Algebra] Determine if a set is a basis

    Determine if {v1,v2,...vn} is a basis of Rn and A is invertible n x n matrix, then {Av1,Av2...Avn} is a basis of Rn

    So I got all the questions before this correct, but this one confusing me.
    I'm not sure what a matrices invertibility has to do with any of this. I do know (i think I know) that if a matrix is invertible then it has linearly independent columns. It looks like {Av1,Av2...Avn} is supposed to be the basis of some matrix transformation but I'm lost on any of the rest of it.
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  2. #2
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    Re: [Linear Algebra] Determine if a set is a basis

    Show that $\displaystyle A v_1,A v_2,\text{...},A v_n$ are linearly independent
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