I'm having trouble with this question.
Here is what I have:
From the hint, we solve the equation first for and then for . So we have
I'm really not sure where to go from here though.
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Well, what does the fact that both and are invertible (so you can write their inverses) say about the last equation you wrote down? Is the transformation invertible?
Ok, I think I understand.
So it is invertible and its inverse is simply:
Is that correct?
I suppose your answer is in keeping with the question's nomenclature in the OP. I would say that is the linear transformation, and that
is the inverse transformation.
I think you get the main mathematical idea, though.
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