Find a basis for the eigenspace corresponding to the eigenvalue λ=2 of the matrix

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- May 18th 2008, 07:47 AMmatty888Basis for eigenspace!
Find a basis for the eigenspace corresponding to the eigenvalue λ=2 of the matrix

A = http://www.cramster.com/Answer-Board...1948056924.gif - May 18th 2008, 08:00 AMIsomorphism
- May 18th 2008, 08:06 AMMoo
Hello,

Solve for in

This yields the following system :

(we can see that these two equations are actually the same).

There are two possibilities. Either y=1, either y=0.

If , then . For example, and

So is an eigenvector of the eigenspace.

If , then . For example, and

So is the second eigenvector of the eigenspace.

Does it look clear ? - May 18th 2008, 08:52 AMmatty888Thanks(????)
Thanks guys just wondering are both of your answers legitimate,I am getting (3,0,4) and (-1,12,0) also, so not really sure????

- May 18th 2008, 09:11 AMIsomorphism
Your answer is right too because from my basis I can represent

So both of your vectors are a linear combination of my basis and your vectors need both of my basis vectors.So your set is a basis :D

You can try getting your vectors as a linear combination of Moo's basis (Nod) - May 18th 2008, 09:14 AMMoo
For my basis, it'll be :

(Wink)