Confusion regarding the basis of A and the basis of Range of A

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SUMMARY

The discussion clarifies the distinction between the basis of a subspace A and the basis of the range of a linear transformation associated with A. A subspace does not possess a "range"; rather, it is the linear transformation that has a range. The confusion arises from textbooks that may conflate these concepts, but they are fundamentally different in linear algebra.

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smithnya
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Hello everyone,

I am having difficulty understanding the difference between the basis of a subspace A and and the basis of the range of A. My textbook seems to follow the same approach in determining both. So are they essentially the same?
 
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I cannot makes sense of your question. You talk about a subspace, A, and then about the range of A. A subspace does not have a "range". A linear transformation has a range.
 

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