Question

Eigenspace of a matrix (question will be below).

Answer 1

I'm looking to find the eigenvalues and corresponding eigenspaces for this matrix:
\[\left[\begin{matrix}1 & 0 & 1 \\ 0 & 1 & 1 \\ 1 & 1 & 0\end{matrix}\right]\]I've got the three eigenvalues -1, 1 and 2 and am having trouble determining the eigenspace for the eigenvalue 1. Anyone able to help?

Answer 2

if i wanted to find a eugene value, how would you talk me thru it?

Answer 3

eugene vector that is, youve already got the values

Answer 4

i would say:

take the value 1, and subtract it from the diagonal

then row reduce the matrix

determine the parametric solutions from the free variables; and the vectors assoiciated with the free variables are your eugene vectors