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saqifriends
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- Jun 13, 2012
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basis for the eigenspace corresponding
- Thread starter saqifriends
- Start date
- Feb 5, 2012
- 1,621
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.
- Feb 15, 2012
- 1,967
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.
(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.