assign9_soln

assign9_soln - Math 136 Assignment 9 Solutions 1. Calculate...

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Math 136 Assignment 9 Solutions 1. Calculate the determinant of the following matrices. a) A = 01 - 10 3 0 0 2 0 1 2 1 5 0 0 7 Solution: Expand along the fourth row: det A = ± ± ± ± ± ± ± ± - 3 0 0 2 0 1 2 1 5 0 0 7 ± ± ± ± ± ± ± ± = - 3 ± ± ± ± ± ± 1 - 121 007 ± ± ± ± ± ± - 5 ± ± ± ± ± ± 1 - 002 ± ± ± ± ± ± =( - 3)(7) ± ± ± ± 1 - 1 12 ± ± ± ± - (5)( - 2) ± ± ± ± 1 - 1 ± ± ± ± = - 21(2 + 1) + 10(2 + 1) = - 63 + 30 = - 33 b) B = 1 - 1 5 5 2 3 1 2 4 6 - 1 - 3 8 0 - 2 1 1 2 - 11 - 1 1 0 Solution: Since adding a multiple of one row to another and adding a multiple of one column to another does not change the determinant, we have det B = ± ± ± ± ± ± ± ± ± ± 1 - 1 5 5 2 3 1 2 4 6 - 1 - 3 8 0 - 2 1 1 2 - - 1 1 0 ± ± ± ± ± ± ± ± ± ± = ± ± ± ± ± ± ± ± ± ± 1 - 1 5 5 2 04 - 13 - 11 0 0 - 4 13 5 0 02 - 3 - 6 - 1 03 - 6 - 4 - 2 ± ± ± ± ± ± ± ± ± ± = ± ± ± ± ± ± ± ± 4 - 13 - 11 0 - 4 13 5 0 2 - 3 - 6 - 1 3 - 6 - 4 - 2 ± ± ± ± ± ± ± ± =6 ± ± ± ± ± ± 4 - 13 0 2 - 3 - 1 3 - 6 - 2 ± ± ± ± ± ± ± ± ± ± ± ± 4 - 13 0 00 - 1 - - 2 ± ± ± ± ± ± ± ± ± ± 4 - 13 - ± ± ± ± = 6( - 13) = - 78 c) C = a b c a + b 2 bc + b 2 2 2 Solution: Since adding a multiple of one row to another does not change the determinant, we have det C = ± ± ± ± ± ± a b c a + b 2 + b 2 2 2 ± ± ± ± ± ± = ± ± ± ± ± ± a b c b b b 2 2 2 ± ± ± ± ± ± = ± ± ± ± ± ± a b c b b b 0 0 0 ± ± ± ± ±
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assign9_soln - Math 136 Assignment 9 Solutions 1. Calculate...

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