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assign5 - the mapping a f x 1,x 2,x 3 = x 1,x 2,x 1 x 2 x 3...

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Math 136 Assignment 5 Due: Wednesday, Feb 16th 1. Calculate the following products or explain why the product is not defined. (a) 1 0 - 2 1 1 2 3 4 - 3 1 3 3 (b) 2 2 - 2 0 1 0 0 1 - 2 2 1 1 2 3 3 (c) 3 1 2 2 1 5 (d) 2 1 5 3 1 2 2. Prove that if A, B, C M m × n ( R ) and s, t R are scalars, then a) A + ( B + C ) = ( A + B ) + C . b) ( s + t ) A = sA + tA . 3. Prove that each of the following mappings are linear and find the standard matrix of
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Unformatted text preview: the mapping. a) f ( x 1 ,x 2 ,x 3 ) = ( x 1 ,x 2 ,x 1 + x 2 + x 3 ) b) f ( x 1 ,x 2 ,x 3 ) = (0 ,x 1-x 2 ) 4. Let A be an m × n matrix. Prove that I m A = A and AI n = A . 5. Prove that if the columns of B are linearly dependent, then so are the columns of AB . 1...
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