Originally Posted by
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!