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Please see the attached file.
1. For each of the following functions decide whether or not the function is a
linear transformation. Prove your answer in each case :
(a) F : V3(R) V2(R), defined by F(a1, a2, a3) = (a1 + a2 + a3, 3a2)
This is a linear transformation. In fact, we can prove
a) For a=(a1, ...
This shows how to determine if a function is a linear transformation.