Homework 9 Solutions

Homework 9 Solutions - EECS 203: Homework 9 Solutions...

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EECS 203: Homework 9 Solutions Section 3.8 1. (E) 4b [ 4 1 7 6 7 5 8 5 4 0 7 3 ] 2. (E) 12a Let A and B be m x k matrices and C be a k x n matrix. By the definition of matrix sum, A+B is an m x k matrix such that each (i,j) entry is equal to a ij + b ij . By definition of matrix product, (A+B)C is an m x n matrix such that each (i,j) entry of (A+B)C is equal to (a i1 +b i1 )c 1j + (a i2 +b i2 )c 2j + … + (a ik +b ik )c kj . This can be rewritten as (a i1 c 1j + a i2 c 2j + … + a ik c kj ) + (b i1 c 1j + b i2 c 2j + … + b ik c kj ). This is equal to the (i,j) entry of AC + BC, which is also an m x n matrix and is therefore equal to (A+B)C. 3. (M) 22 By the result of exercise 17b, (AA t ) t = (A t ) t A t . Note that (A t ) t = A, since the switching rows and columns twice yields the original matrix (as seen in exercise 16). So, (AA t ) t = AA t . Since AA t is equal to its transpose, it must be symmetric, since each element a ij is equal to a ji . 4. (E) 24b
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Homework 9 Solutions - EECS 203: Homework 9 Solutions...

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