# Find basis

• 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

• 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

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 $\{ (1,1,0),(1,0,1)\}$