h7 - A = [ T ] C B of T with respect to these bases. (b)...

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Homework Set 7 for MAS 4105 Due Wednesday, February 29 1. Let A and B be n × n matrices such that AB is invertible. Prove that A and B are both invertible. 2. Give an example of matrices A and B such that AB is invertible but BA is not invertible. (Hint: First try to guess the sizes of A and B .) 3. De±ne T : P 1 ( R ) R 2 by T ( f ) = ( f (1) , f ( - 1)). (a) Choose bases B for P 1 ( R ) and C for R 2 and compute the matrix
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Unformatted text preview: A = [ T ] C B of T with respect to these bases. (b) Show that the matrix A is invertible and compute A-1 . (c) Use (b) to give a formula for T-1 ( x 1 , x 2 ). The following problems are strongly recommended, but should not be turned in: 2.4: 1, 2, 3, 4, 5, 7, 8, 9, 12, 13, 14, 16, 17, 18...
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This note was uploaded on 03/27/2012 for the course MAS 4105 taught by Professor Rudyak during the Spring '09 term at University of Florida.

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