Question

any able to help with eigenvectors? question in thread.

Answer 1

\[A=\left[\begin{matrix}0 & 1 & 1 \\ 1 & 0 & 1 \\ 1& 1 & 0\end{matrix}\right]\]
i found the eigen values to be \( \lambda_{1,2}=-1\) and \(\lambda_{3}=2 \), I know i need to do \((A-\lambda I)=0\) but i am stuck on the resulting system of equations.

Answer 2

after you find the eigenvalues, you find the null space of (A−λI) to find the eigenvectors

for λ=−1
\[(A−λI)=\left[\begin{matrix}1 & 1 & 1 \\ 1 &1 & 1 \\ 1& 1 & 1\end{matrix}\right] \]
reduce to rref (reduced row echelon form)

\[(A−λI)=\left[\begin{matrix}1 & 1 & 1 \\ 0 &0 & 0 \\ 0& 0 & 0\end{matrix}\right] \]
the vectors in the null space are (-1 1 0) and (-1 0 1)

Answer 3

do the same for λ=2

Answer 4

@phi thanks