Find eigenvalues and eigenvectors for the matrix $\left[\begin{array}{cc} -6 &-7\cr 14 &15 \end{array}\right]$.

The smaller eigenvalue has an eigenvector $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$.
The larger eigenvalue has an eigenvector $\left[\Rule{0pt}{2.4em}{0pt}\right.$$\left]\Rule{0pt}{2.4em}{0pt}\right.$.