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# 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 = 1 2 - 1 3 - 2 - 1 , B = 1 0 0 0 2 - 3 , C = 5 - 1 2 1 - 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 ) x = 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 , x 3 ) = ( x 1 + x 2 + 1 , x 3 , 0). b) f ( x 1 , x 2 ) = (0 , x 1 + 2 x 2 , x 2 ). c) proj ( - 2 , 1) . 4. Determine the standard matrix of a reflection 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 [ kL + M ] = k [ L ] + [ M ]. 6. Suppose that S and T are linear mappings with matrices [ S ] = 4 - 3 1 1 5 - 3 - 2 0 [ T ] = 4 0 2 3 - 2 1 3 0 . a) Determine the domain and codomain of each mapping. b) Determine the standard matrices that represent
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