Find a basis for the eigenspaceE2, corresponding to the eigenvalue λ = 2 of the matrix

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- May 20th 2008, 06:40 AMmatty888Find basis
Find a basis for the eigenspace

**E2**, corresponding to the eigenvalue λ = 2 of the matrix

**B =**http://www.cramster.com/Answer-Board...8062506876.gif - May 20th 2008, 07:11 AMIsomorphism
Essentially solve $\displaystyle Bx = 2x $ where x = [a;b;c].

So $\displaystyle -a + b + c = 0$, Thus the general form of the vectors in the eigenspace are $\displaystyle (x+y,x,y)$ and its dimension is 2.

So one of the basis is $\displaystyle \{ (1,1,0),(1,0,1)\}$