Basis for the eigenspace corresponding

[saqifriends]

View attachment 213

 

[Sudharaka]

View attachment 213

Hi saqifriends, :)

I have outlined the method to do this kind of problems http://www.mathhelpboards.com/threads/1270-basis-for-each-eigenspace?p=6086&viewfull=1#post6086 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]

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.