I'm having trouble with this question.

http://img585.imageshack.us/img585/1729/243m.png

Here is what I have:

From the hint, we solve the equation first for and then for . So we have

so...

I'm really not sure where to go from here though.

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- Mar 1st 2011, 02:59 PMcentenialIs the linear transformation y = A(Bx) invertible?
I'm having trouble with this question.

http://img585.imageshack.us/img585/1729/243m.png

Here is what I have:

From the hint, we solve the equation first for and then for . So we have

so...

I'm really not sure where to go from here though. - Mar 1st 2011, 06:30 PMAckbeet
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?

- Mar 1st 2011, 07:01 PMcentenial
Ok, I think I understand.

So it is invertible and its inverse is simply:

Is that correct? - Mar 1st 2011, 07:10 PMAckbeet
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.