Solutions4 - Math 601 Solutions to Homework 4 1. Use row...

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 601 Solutions to Homework 4 1. Use row reduction to compute the determinants of the following ma- trices: (a) A = 1 1 3 2 1 3 11 12 2 1 3 6 4 2 5 8 (b) B = a a a a a a b 2 b b b b b c c 3 c c c c d d d 4 d d d e e e e 5 e e 1 1 1 1 1 6 Answer: (a) We row reduce the matrix: 1 1 3 2 1 3 11 12 2 1 3 6 4 2 5 8 - row 1- 2 row 1- 4 row 1- 1 1 3 2 2 8 10- 1- 3 2- 2- 7 1 2 1 1 3 2 1 4 5- 1- 3 2- 2- 7 + row 2 +2 row 2- 1 1 3 2 1 4 5 1 7 1 10 - row 3- 1 1 3 2 1 4 5 1 7 3 The determinant of the row reduced matrix is 3 (because the ma- trix is triangular, so the determinant is the product of the di- agonal entries). Most of the row operations did not change the determinant. When we multiplied the second row by 1 2 , we also multiplied the determinant by 1 2 . This is the only row operation that changed the determinant. Thus, the original matrix, had determinant 2 3 = 6. Thus, det( A ) = 6 (b) We can begin by dividing the first row by a , the second row by b , the third row by c , the fourth row by d , and the fifth row by e . We get: fl fl fl fl fl fl fl fl fl fl fl fl a a a a a a b 2 b b b b b c c 3 c c c c d d d 4 d d d e e e e 5 e e 1 1 1 1 1 6 fl fl fl fl fl fl fl fl fl fl fl fl = abcde fl fl fl fl fl fl fl fl fl fl fl fl 1 1 1 1 1 1 1 2 1 1 1 1 1 1 3 1 1 1 1 1 1 4 1 1 1 1 1 1 5 1 1 1 1 1 1 6 fl fl fl fl fl fl fl fl...
View Full Document

Page1 / 7

Solutions4 - Math 601 Solutions to Homework 4 1. Use row...

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