Let F be an affine map. Prove that the corresponding linear map is unique.
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1. Since f:E->E' is an affine map, we want to show the corresponding
linear map v(f) is unique. Suppose we have two linear maps v(f) and
v'(f), then for any x in E, we have
f(x)=v(f)x+b=v'(f)x+b', where b,b' are in E'
Then f(0)=b=b'. ...
This is a series of three proofs regarding affine maps.