Unformatted text preview: f ( e 1 + e 2 )f ( e 1 ) = ± 1 1 ²± 3 3 ² =2 ± 1 1 ² . Therefore, by Theorem 2, If there is such a linear transformation f , it must be given by the matrix A f = ± 32 32 ² . ( * ) So far, we have used the ﬁrst 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 ³± 1 2 ²´ = ± 3 3 3 1 ²± 1 1 ² . This is not the case: The right side is ±11 ² , and we are told that the left side is ± 3 1 ² . 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, The Matrix Reloaded, The Matrix Revolutions, Wachowski brothers, linear transformation, Keanu Reeves, IR2

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