Question

Help with eigenvalues and eigenspace.

Answer 1

I found the eigenvalues to 1,2,3. But how do I find the eigenspace?

Answer 2

@Loser66 multiplicity of roots

Answer 3

1,2,2,3

Answer 4

For each eigenvalue you have an eigenspace which consists of the eigenvectors for that eigenvalue and all their scalar multiples... so all you need to find are eigenvectors. Can you do that?

Answer 5

λ*v?

Answer 6

Find the eigenvectors for each eigenvalue... these are the basis vectors for that eigenvalue's associated eigenspace

Answer 7

Like this:

Answer 8

for the first one, you have 2x=0, 4x=0 , y +z=0 and t =0, so the eigenvector correspond to eigenvalue 1 is \[\left(\begin{matrix}0\\-z \\z\\0\end{matrix}\right), take z out, z\left(\begin{matrix}0 \\ -1\\1\\0\end{matrix}\right)\]

Answer 9

that is the first basis eigenspace of eigenvalue 1.

Answer 10

find out the leftover by that way. hihi... that's all i know, but you should way for oldrin.bataku. to get the right answer. Mine just for fun

Answer 11

I find the eigenspace this way, right?
\[E_{\lambda}=N(\lambda I_{n}-A)\]