The matrix $$A = \left[\begin{array}{ccc} 10 &0 &-14\cr -14 &-4 &14\cr 7 &0 &-11 \end{array}\right]$$ has $\lambda = -4$ as an eigenvalue with multiplicity $2$ and $\lambda = 3$ as an eigenvalue with multiplicity $1$. Give one associated eigenvector for each of the eigenvalues.

The eigenvalue $-4$ has associated eigenvector $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.

The eigenvalue $3$ has associated eigenvector $\left[\Rule{0pt}{3.6em}{0pt}\right.$$\left]\Rule{0pt}{3.6em}{0pt}\right.$.