Find basis

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• May 20th 2008, 06:40 AM
matty888
Find 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 AM
Isomorphism
Quote:

Originally Posted by matty888
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

Essentially solve $Bx = 2x$ where x = [a;b;c].

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

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