What are Eigenvectors and Eigenvalues?

[flyingpig]

Homework Statement

http://img820.imageshack.us/img820/4874/cah.th.png

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The Attempt at a Solution

a) Did it already, 3 is the eigenvalue

b) This is just finding the nullspace and the basis of the nullspace are my eigenvectors right?

c) ignore this one, we cover this next term

 

[Mark44]

Homework Statement

http://img820.imageshack.us/img820/4874/cah.th.png

Uploaded with ImageShack.us

The Attempt at a Solution

a) Did it already, 3 is the eigenvalue

b) This is just finding the nullspace and the basis of the nullspace are my eigenvectors right?

This is simpler than you seem to be making it out to be. If 0 is an eigenvalue, then det(A) = 0, and Ax = 0x for any eigenvector of 0.

c) ignore this one, we cover this next term

 

[flyingpig]

Wait for b)

Ax = λx = 0x = 0

Ax = 0 <=== not nullspace?

Are you implying that

det(Ax) = det(0I) = 0

det(Ax) = 0

How do you pull the x out?

 

[Mark44]

Wait for b)

Ax = λx = 0x = 0

Ax = 0 <=== not nullspace?

Are you implying that

det(Ax) = det(0I) = 0

det(Ax) = 0

How do you pull the x out?

You can't just move a bunch of symbols around. You need to do something with your matrix A.

$$\begin{bmatrix}2&-1&1\\-1&2&1\\1&1&2\end{bmatrix}$$

 

[flyingpig]

RowReduce...