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June 18th, 2010, 11:50 AM   #1
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affine transformation

how to solve this?

an affine transformation theta:R^n -->R^n acts as follow: theta(x) = 2*x+v, for all x in R^n, v is a constant vector;

An affine subspace B in R^n is the set of solutions to the equation f(x)=c, where f: R^n-->R is a nonzero linear map and c is an arbitrary constant.
Find the equation of theta(B), where theta(B) is defined as the set of theta(x) for all x in B.


...what I can conclude is, f(x)=2*x, then I find x and the set B, but how to find theta(B)? is it the composition of two affine transformations?

thanx
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