Confused on finding Eigenvalues and Eigenvectors

1. Oct 23, 2005

mr_coffee

confused on finding Eigenvalues and Eigenvectors!!

hello everyone, i can't understand this example, how did they find the Eigen value of 3?! Aslo an Eigen vector of 1 1? http://img438.imageshack.us/img438/1466/lastscan1oc.jpg
thanks.

2. Oct 23, 2005

iNCREDiBLE

3. Oct 23, 2005

mr_coffee

4. Oct 23, 2005

Muzza

You've factored it incorrectly.

5. Oct 23, 2005

mr_coffee

i know, i can't factor that and get a nice number, i'd have to use the quadtract equation, but that can't be right because the book got a nice answer of 3.

6. Oct 23, 2005

TD

As Muzza said, only the factoring was wrong!

$$\lambda ^2 - 4\lambda + 3 = \left( {\lambda - 1} \right)\left( {\lambda - 3} \right) \ne \left( {\lambda - 4} \right)\left( {\lambda + 1} \right)$$

7. Oct 23, 2005

mr_coffee

ohhh wow i suck hah, thank u so much!! why did they only use $$\lambda = 3$$ when it can also equal 1?

8. Oct 23, 2005

HallsofIvy

Staff Emeritus
Even knowing that one solution was 3, so one factor must be x- 3 you couldn't factor it??

Read it carefully! It specifically says "an eigenvalue", not the eigenvalue. And immediately below states that there is another and solves for it.

9. Oct 23, 2005

mr_coffee

This is what we witnessed today. :surprised
To think i have a 3.77 GPA. What is the world coming too?
Anywho, thanks for the explanation everyone.

Last edited: Oct 23, 2005