(a) Find the value of \(a\) for which the system of equations
\[\begin{array}{r}
13 x+18 y-28 z=0 \\
-4 x-a y+8 z=0 \\
2 x+6 y-5 z=0
\end{array}\]
does not have a unique solution.

The matrix \(\mathbf{A}\) is given by
\[\mathbf{A}=\left(\begin{array}{rrr}
13 & 18 & -28 \\
-4 & -1 & 8 \\
2 & 6 & -5
\end{array}\right)\]
(b) Find the eigenvalue of \(\mathbf{A}\) corresponding to the eigenvector \(\left(\begin{array}{l}2 \\ 0 \\ 1\end{array}\right)\).
(c) Find a matrix \(\mathbf{P}\) and a diagonal matrix \(\mathbf{D}\) such that \(\mathbf{A}=\mathbf{P D P}^{-1}\).

(d) Use the characteristic equation of \(\mathbf{A}\) to find \(\mathbf{A}^{-1}\) in terms of \(\mathbf{A}\).