assign9_soln

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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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...
View Full Document

Page1 / 5

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online