assign9_soln

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

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Unformatted text preview: Math 136 Assignment 9 Solutions 1. Calculate the determinant of the following matrices. a) A = 0 1- 1 0 3 0 2 0 1 2 1 5 0 7 Solution: Expand along the fourth row: det A = 0 1- 1 0 3 0 2 0 1 2 1 5 0 7 =- 3 1- 1 0 1 2 1 7- 5 1- 1 0 2 1 2 1 = (- 3)(7) 1- 1 1 2- (5)(- 2) 1- 1 1 2 =- 21(2 + 1) + 10(2 + 1) =- 63 + 30 =- 33 b) B = 1- 1 5 5 2 3 1 2 4 6- 1- 3 8- 2 1 1 2- 1 1 1 2- 1 1 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- 2 1 1 2- 1 1 1 2- 1 1 = 1- 1 5 5 2 4- 13- 11- 4 13 5 2- 3- 6- 1 3- 6- 4- 2 = 4- 13- 11- 4 13 5 2- 3- 6- 1 3- 6- 4- 2 = 6 4- 13 2- 3- 1 3- 6- 2 = 6 4- 13- 1- 1- 2 = 6 4- 13- 1 = 6(- 13) =- 78 c) C = a b c a + b 2 b c + 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 c + b 2 2 2 = a b c b b b 2 2 2 = a b c b b b 0 0 0 = 0 ....
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This note was uploaded on 05/04/2010 for the course MATH 136 taught by Professor All during the Spring '08 term at Waterloo.

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

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