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assign5 - Math 136 Assignment 5 Due Wednesday Feb 15th 1...

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Math 136 Assignment 5 Due: Wednesday, Feb 15th 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. Find t 1 , t 2 , t 3 R such that t 1 1 1 0 1 + t 2 2 0 0 2 + t 3 0 2 - 1 1 = 6 3 3 3 3. Determine which of the following mappings are linear. Find the standard matrix, a basis for the kernel, and a basis for the range 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 ~a where ~a = - 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
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