|Mar17-10, 07:49 PM||#1|
Linear Algebra - Bilinear Forms and Change of Basis
1. The problem statement, all variables and given/known data
Find the matrix of f relative to Alpha' and Beta'.
Alpha' = [(1,0,0), (1,1,0), (2,-1,1)]
Beta' = [(-13,9), (10,-7)]
The question originally reads that f is a bilinear form.
I've found a (correct according to answer key) matrix A that is
from a given basis of
Alpha = [(1,0,0), (1,1,0), (1,1,1)] and
Beta = [(1,-1), (2,-1)]
2. Relevant equations
If Q is the matrix of transition from Alpha to basis Alpha' of U and P is the matrix of transition from Beta to basis Beta' of V, then QTAP = matrix of f relative to Alpha' and Beta'.
T meaning transpose.
3. The attempt at a solution
I've gotten oh so far with this question, but I'm stuck here in the final part. I'm confused how to attain said matrices Q and P from the relevant equations. If I'm not terrible mistaken, I think I have to do something involving inverses but I'm at a loss here.
Any help will of course be greatly appreciated.
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