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 = 7 1- 1 1 3 3- 4 5 3 2 1 4 1 1- 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 A = 7 1- 1 1 3 3- 4 5 3 2 1 4 1 1- 1 1 =- 6 6- 6- 1 2- 1 4 1 1 1- 1 1 = (- 1)- 6 6- 6- 1 2- 1 4 1 = (- 1)- 6 6- 1 2- 1 9 = (- 1)(- 1)- 6 6- 1 9 = (- 6)(9)- (6)(- 1) =- 48 b) B = 2 3 2- 2 3 1 4 1 1 2 4 4 2- 1 5 6 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 2 3 2- 2 3 1 4 1 1 2 4 4 2- 1 5 6 =- 1- 6- 10- 5- 8- 11 1 2 4 4- 5- 3- 2 =- 1- 6- 10- 5- 8- 11 1 2 4 4- 5- 3- 2 =- 1- 6- 10- 5- 8- 11- 5- 3- 2 =- 1- 6- 10 22 39 5 9 = (- 1) 22 39 5 9 = (- 1)[(29)(9)- 39(5)] = 3 c) C = 1- 1 i 1 + i- i i 1- i- 1 + 2 i 1 + 2 i Solution: Since adding a multiple of one row to another does not change the determinant, we have det D = 1- 1 i 1 + i- i i 1- i- 1 + 2 i 1 + 2 i = 1- 1 i 1 + i- i i 1- i- 1 + 2 i 1 + 2 i = 1- 1 i 1 1 i i = 1- 1 i 1 1 Hence det D = 0....
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assign9_soln - Math 136 Assignment 9 Solutions 1. Calculate...

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