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 = 2- 4 0 0 1- 2 2 9- 3 6 0 3 1- 1 0 0 Solution: Expanding along the third column gives det A = 2- 4 0 0 1- 2 2 9- 3 6 0 3 1- 1 0 0 = (- 1)(2) 2- 4 0- 3 6 3 1- 1 0 Expanding along the third column again we get det A = (- 2)(- 1)(3) 2- 4 1- 1 = 6(- 2 + 4) = 12 b) B = 1 10 7- 9 7- 7 7 7 2- 2 6 2- 3- 3 4 1 Solution: Using row operations to simplify the determinant we get det B = (7) 1 10 7- 9 1- 1 1 1 2- 2 6 2- 3- 3 4 1 = 7 11 6- 10 1- 1 1 1 4- 6 7 4 Expanding along the third row we get det B = (7)(4) 11- 10 1- 1 1- 6 4 Now expanding along the first column gives det B = 28(- 1) 11- 10- 6 4 = (- 28)(44- 60) = 448 1 2 c) C = 1 a a 2 a 3 1 b b 2 b 3 1 c c 2 c 3 1 d d 2 d 3 Solution: We have det C = 1 a a 2 a 3 b- a b 2- a 2 b 3- a 3 c- a c 2- a 2 c 3- a 3 d- a d 2- a 2 d 3- a 3 = b- a b 2- a 2 b 3- a 3 c- a c 2- a 2 c 3- a 3 d- a d 2- a 2 d 3- a 3 = ( b- a )( c- a )( d- a ) 1 b + a b 2 + ba + a 2 1 c + a c 2 + ca + a 2 1 d + a d 2 + da + a 2 = ( b- a )( c- a )( d- a ) 1 b + a b...
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assign9_soln - Math 136 Assignment 9 Solutions 1 Calculate...

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