Please see Attachment Respond in PDF format© BrainMass Inc. brainmass.com March 4, 2021, 6:08 pm ad1c9bdddf
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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 ...
This looks at whether vector spaces are one-to-one or onto.