6.1 - Math 2940 Solutions, Fall 2011 Section 6 . 1 5 ) det...

Info iconThis preview shows pages 1–2. 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 2940 Solutions, Fall 2011 Section 6 . 1 5 ) det 3- 1 1- = (3- )(1- ) has roots = 1 , 3. det 1- 1 3- = (1- )(3- ) has roots = 1 , 3. det 4- 1 1 4- = (4- ) 2- 1 = 2- 8 + 15 = ( - 5)( - 3) has roots = 5 , 3. The eigenvalues of a sum of matrices are not the sum of the eigenvalues of the matrices. Actually it doesnt even make sense - there are four possible sums of the eigenvalues of A and B but only two eigenvalues for A + B . 10 ) det . 6- . 2 . 4 . 8- = 2- 1 . 4 + . 4 = ( - 1)( - . 4) has roots = 1 , . 4. An eigenvector for = . 4 is (1 ,- 1) and an eigenvector for = 1 is (1 , 2). det (1 / 3)- 1 / 3 2 / 3 (2 / 3)- = 2- = ( - 1) has roots = 0 , 1. An eigenvector for = 0 is (1 ,- 1) and an eigenvector for = 1 is (1 , 2). So A 100 has eigenvalues 1 and ( . 4) 100 , which is close to 0. So A 100 and A have very close eigenvalues (and it is not a repeated eigenvalue) so they should have very close eigenvectors.eigenvalues (and it is not a repeated eigenvalue) so they should have very close eigenvectors....
View Full Document

This note was uploaded on 01/02/2012 for the course MATH 2940 at Cornell University (Engineering School).

Page1 / 2

6.1 - Math 2940 Solutions, Fall 2011 Section 6 . 1 5 ) det...

This preview shows document pages 1 - 2. Sign up to view the full document.

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