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[Community Question] Linear-algebra: T/F: The Range of a Linear Transformation must be a subset of the domain.

One of our user asked:

I am having difficulty understanding why it is false. As I understand, the range is the output of everything from the domain into the transformation function, or the result of the domain being outputted to the co-domain via the transformation. Essentially, I cannot think of a counterexample where the range of a linear transformation is not in the domain. I would appreciate if anyone could shed some light on this basic concept that I am struggling with.


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