Finding Eigenvectors & Eigenvalues of A Matrix

[innightmare]

Homework Statement

Use direct multiplication to show that for each of the following matrices A, the given vectors v1, v2, and v3 are eigenvectors of A and to find the eigen values lama1, lama2, and lama3 of A:

A=top row: (2 -1 3) second row: (-1 6 -1) third row: (3 -5 2) v1=(1,0,-1) v2=(2,2,2), v3 =(7, -9,11)

Homework Equations

Plug the v's back into the A matrice

The Attempt at a Solution

Have no idea what they mean nor how to go about the direct multiplication here. Thanks What exactly do they want me to do?

 

[malawi_glenn]

matrix * vector = eigenvalue * (same)matrix

 

[CompuChip]

matrix * vector = eigenvalue * (same)vector

There's a minor (typo) error in there, see the correction in bold

 

[malawi_glenn]

yeah LOL :)

otherwise it would have been called eigenmatrix ;)