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**Oijl** Hi. My Linear Algebra with Applications, 4th Ed. by Otto Bretscher (Pearson International Edition) poses the following exercise:

Consider linearly independent vectors v1, v2, ..., vm in R(n), and let A be an invertible mxm matrix. Are the columns of the following matrix linearly independent?

[v1 | v2 | ... | vm]A

What I know relevant to linear independence is that the following statements are equivalent, for a list v1, v2, ..., vm of vectors in R(n):

1. Vectors v1, v2, ..., vm are linearly independent

2. None of the vectors v1, v2, ..., vm is redundant

3. ker[v1 | v2 | ... | vm] = {0}

4. rank[v1 | v2 | ... | vm] = m

Can anyone give me pointers in what to be looking at in order to answer this question?

Thanks!