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mat67-2011-hw6solutions

# mat67-2011-hw6solutions - Solutions to HW#6 Math 67 UC...

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Solutions to HW #6 Math 67 UC Davis, Fall 2011 1. For each of the following pairs of matrices A, B , compute the matrix product AB and the matrix product BA , or for each of these products indicate if it is undefined. (a) A = 1 2 3 6 5 4 , B = 0 - 1 1 1 2 2 Solution. AB = 8 7 13 7 , BA = - 6 - 5 - 4 7 7 7 14 14 14 (b) A = 1 2 3 0 - 3 1 0 0 - 1 , B = 6 0 0 - 1 1 0 1 0 1 Solution. AB = 7 2 3 4 - 3 1 - 1 0 - 1 , BA = 6 12 18 - 1 - 5 - 2 1 2 2 (c) A = ( 1 2 ) , B = 4 7 Solution. AB = ( 18 ) BA = 4 8 7 14 (d) A = 1 2 3 6 5 4 , B = ( 0 0 ) Solution. AB = undefined , BA = ( 0 0 0 ) 2. For each of the following matrices, find if the matrix is invertible, and if it is, compute the inverse matrix. Check your answer by multiplying the matrix by its purported inverse. (a) A = 1 2 3 4 = A - 1 = - 2 1 3 2 - 1 2 (b) A = 1 2 3 0 1 1 0 0 - 1 = A - 1 = 1 - 2 1 0 1 1 0 0 - 1 (c) A = 1 2 6 1 0 1 3 0 0 0 1 0 0 2 6 1 = A - 1 = 1 0 0 - 1 0 1 - 3 0 0 0 1 0 0 - 2 0 1 1

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Solutions to HW #6 Math 67 UC Davis, Fall 2011 3. Write down the 24 different permutations of order 4. For each one, find the inversion
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mat67-2011-hw6solutions - Solutions to HW#6 Math 67 UC...

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