# basis for the eigenspace corresponding

#### Sudharaka

##### Well-known member
MHB Math Helper
Hi saqifriends,

I have outlined the method to do this kind of problems here. Since you have been given a particular eigenvalue, find the eigenspace corresponding to that eigenvalue. Then find a basis for that eigenspace.

Kind Regards,
Sudharaka.

#### Deveno

##### Well-known member
MHB Math Scholar
as a slight nudge towards the answer, solve the system:

(A - λI)v = 0. in this case, λ = 3, so you must find the null space of the matrix:

$\begin{bmatrix}1&2&3\\-1&-2&-3\\2&4&6 \end{bmatrix}$

the rank of this matrix should be obvious upon inspection, and the rank-nullity theorem then tells you how many basis vectors you should have for the null space.