Is there a linear algebra theorem or fact that says something like(adsbygoogle = window.adsbygoogle || []).push({});

For a linear transformation T:Rn -> Rm and its standard m x n matrix A:

(a) If the columns of A span Rn the transformation is onto.

(b) If the columns of A are linearly independent the transformation is one-to-one.

Is this correct? I can't find it anywhere in my textbook but it may have been mentioned in lecture. Any insight would be appreciated.

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# Homework Help: Linear independence and span

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