5.1soln

# 5.1soln - Solutions to problems from section 5.1 6. Is 1- 2...

This preview shows pages 1–2. Sign up to view the full content.

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Solutions to problems from section 5.1 6. Is 1- 2 1 an eigenvector of 3 6 7 3 3 7 5 6 5 ? If so, find the eigenvalue. Solution: 3 6 7 3 3 7 5 6 5 1- 2 1 = - 2 4- 2 =- 2 1- 2 1 so 1- 2 1 is an eigenvector of 3 6 7 3 3 7 5 6 5 with eigenvalue- 2. 8. Is λ = 3 and eigenvalue of A = 1 2 2 3- 2 1 1 1 ? If so, find one corresponding eigenvector. Solution: Let’s look at the augmented matrix corresponding to the system ( A- 3 I 3 ) x = : - 2 2 2 3- 5 1 1- 2 NR 1 =- 1 2 R 1-→ 1- 1- 1 0 3- 5 1 1- 2 0 NR 2 = R 2- 3 R 1-→ 1- 1- 1- 2 4 1- 2 NR 2 =- 1 2 R 2-→ 1- 1- 1 0 1- 2 0 1- 2 0 NR 3 = R 3- R 2 NR 1 = R 1 + R 2-→ 1 0- 3 0 0 1- 2 0 0 0 0 0 . Thus there is a nontrivial solution to ( A- 3 I 3 ) x = (i.e. an eigenvector of eigenvalue 3) so 3 is a n eigenvalue. We can also list all 3-eigenvectors using our reduced matrix above as all3 is a n eigenvalue....
View Full Document

## This note was uploaded on 01/28/2010 for the course MATH 307 taught by Professor Axenovich during the Fall '08 term at Iowa State.

### Page1 / 3

5.1soln - Solutions to problems from section 5.1 6. Is 1- 2...

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

View Full Document
Ask a homework question - tutors are online