A=\left(\begin{array}{cc}

-7 & -6 \\

-6 & -7

\end{array}\right) Eigenvalues of A: \lambda_{1}, \lambda_{2}= Eigenvector for the lower eigenvalue: \left(\begin{array}{l}

x \\

y

\end{array}\right)= Reminder: check the formatting instructions above. B=\left(\begin{array}{cc}

14 & -18 \\

-18 & -1

\end{array}\right) Eigenvalues of B: \lambda_{1}, \lambda_{2}= Eigenvector for the lower eigenvalue: \left(\begin{array}{l}

x \\

y

\end{array}\right)= Eigenvector for the higher eigenvalue: \left(\begin{array}{l}

x \\

y

\end{array}\right)= Check that the eigenvectors in each case are orthogonal by calcuating the scalar product. Why should you expect(or not expect) that each matrix will have orthogonal eigenvectors? (a) The matrices each have an inverse.(b) The matrices are square.(c) It is by pure luck that this is the case.(d) The matrices are symmetric.