assign5 - Math 136 Assignment 5 Due: Wednesday, Feb 24th 1....

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Math 136 Assignment 5 Due: Wednesday, Feb 24th 1. Let A = ± 12 - 1 3 - 2 - 1 ² , B = ± 1 0 0 02 - 3 ² , C = ± 5 - 1 - ² . Determine the following a) 2 A - B b) A ( B T + C T ) c) BA T + CA T 2. Prove that if ±x M (3 , 2) and a,b R are scalars, then ( a + b ) = a±x + b±x . 3. Determine which of the following mappings are linear. Find the standard matrix of each linear mapping. a) f ( x 1 ,x 2 3 ) = ( x 1 + x 2 +1 3 , 0). b) f ( x 1 2 ) = (0 1 +2 x 2 2 ). c) proj ( - 2 , 1) . 4. Determine the standard matrix of a re±ection in R 2 in the line x 1 - 5 x 2 = 0. 5. Let L and M be linear mappings from R n to R m , and let k R . a) Prove that L + M and kL are linear mappings. b) Prove that [ + M ]= k [ L ]+[ M ]. 6. Suppose that S and T are linear mappings with matrices [ S 4 - 3 11 5 - 3 - 20 [ T ± 4 0 2 3 - 2130 ² . a) Determine the domain and codomain of each mapping. b) Determine the standard matrices that represent
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This note was uploaded on 04/30/2010 for the course MATH 136 taught by Professor All during the Winter '08 term at Waterloo.

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