# Transformation

Please see Attachment Respond in PDF format

© BrainMass Inc. brainmass.com October 9, 2019, 4:24 pm ad1c9bdddfhttps://brainmass.com/math/linear-transformation/transformation-vector-spaces-31490

#### Solution Preview

Please see attached file.

If A is 1 to 1, i.e., Ax=0 if and only if x=0, then the columns of A are linearly independent by definition.

To show this in more details, let's look at the following:

The Definition of ...

#### Solution Summary

This looks at whether vector spaces are one-to-one or onto.

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