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Unformatted text preview: X i =1 -i = 1 -1 Now, let T : R R be a linear transformation with R regarded as a Q-vector space (i.e. T is additive, and homogeneous with respect to rational scalars). Then: X i =1 T ( -i ) = T 1 -1 [NOTE: Lets say that a real number r is transcendental i 6 p ( x ) P ( Q )( p ( r ) = 0). If necessary, you may use, without proof, the fact that is transcendental.] 6. If A and B are ( m n )- and ( n m )-matrices, respectively, then even though AB and BA have dierent dimensions, both are square, and det( AB ) = det( BA )....
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This note was uploaded on 03/28/2012 for the course MATH 110 taught by Professor Gurevitch during the Fall '08 term at Berkeley.
- Fall '08