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Unformatted text preview: f ( e 1 + e 2 )f ( e 1 ) = 1 1  3 3 =2 1 1 . Therefore, by Theorem 2, If there is such a linear transformation f , it must be given by the matrix A f = 32 32 . ( * ) So far, we have used the rst and third pieces of given information about f . Is the second piece of information consistent? By Theorem 5 and ( * ), if f were linear, we would have to have f 1 2 = 3 3 3 1 1 1 . This is not the case: The right side is 11 , and we are told that the left side is 3 1 . Hence the three pieces of information are inconsistent with f being linear, and so there is no such linear transformation. 21 /september/ 2005; 22:09 14...
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 Fall '08
 Gladue
 Calculus

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