(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

http://img847.imageshack.us/img847/2783/77597781.jpg [Broken]

2. Relevant equations

See below.

3. The attempt at a solution

I get all the way to the last step, but I'm not sure how to perform it.

I get to the point where I have:

[(T^-1)(ax^2+bx+c)][itex]\alpha[/itex]= [T^-1][itex]\alpha\beta[/itex]*[v][itex]\beta[/itex]=

[ a/4 + b/8 - (3c/8)]

[ 3(b+c) - (a/2) ]

[(a/2) - ((b+c)/4) ]

Now, at this point, I need to get those 3 elements into a 2x2 symmetric matrix. At first I just made the top element the repeated element along the diagonal, but apparently this is wrong.

At this point on my homework my teacher wrote, "Now use [itex]\alpha[/itex]={basis v1, basis v2, basis v3} (the given basis in the problem statement).

I'm still not sure exactly what to do at this point. I don't know how to get those three elements into a 2x2 symmetric matrix "under" the basis alpha.

Can someone please show me how to perform this last step? Thanks! :)

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# Matrix Problem From Hell - Inverse of Linear Transformation

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