# Math Help - basis for the eigenspace

1. ## basis for the eigenspace

| -3 , 0 , 0, 0 |
| 0 , 2, 1 , 0| = A
| 0 , 0, 2, 0 |
| 0 , 0 , 0 , 2|

The characteristic polynomial of A is (t + 3)(t − 2)^3. Find a basis for the eigenspace of A corresponding to the
eigenvalue λ = 2.

{[0,1,0,0]^T, [0,0,0,1]^T}

Any help would be appreciated.

2. ## Re: basis for the eigenspace

Have you tried just using the DEFINITIONS?

An eigenvector, v, of A with eigenvalue 2 must satisfy Ax= 2x so
$\begin{bmatrix} 3 & 0 & 0 & 0 \\ 0 & 2 & 1 & 0 \\ 0 & 0 & 2 & 0 \\ 0 & 0 & 0 & 2 \end{bmatrix}\begin{bmatrix} x \\ y \\ z \\ u\end{bmatrix}= \begin{bmatrix} 2x \\ 2y \\ 2z \\ 2u\end{bmatrix}$
which gives the equations -3x= 2x, 2y+ z= 2y, 2z= 2z, 2u= 2u. What do you get when you try to solve those equations?

3. ## Re: basis for the eigenspace

I am, however, concerned about your choice of username: "killingphil". Whose is this "phil" and why are you so angry at him?