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tandoorichicken
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Is there a linear algebra theorem or fact that says something like
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.
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.