Find the inverse of each of the following matrices, if possible, by applying the GaussJordan Method.
(a) $\left(\begin{array}{ll}1 & -2 \\ 3 & -3\end{array}\right)$,
(b) $\left(\begin{array}{ll}1 & 3 \\ 3 & 1\end{array}\right)$,
(c) $\left(\begin{array}{rr}\frac{3}{5} & -\frac{4}{5} \\ \frac{4}{5} & \frac{3}{5}\end{array}\right)$,
(d) $\left(\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 7 & 8 & 9\end{array}\right)$,
(e) $\left(\begin{array}{rrr}1 & 0 & -2 \\ 3 & -1 & 0 \\ -2 & 1 & -3\end{array}\right)$,
(f) $\left(\begin{array}{lll}1 & 2 & 3 \\ 3 & 5 & 5 \\ 2 & 1 & 2\end{array}\right)$,
(g) $\left(\begin{array}{rrr}2 & 1 & 2 \\ 4 & 2 & 3 \\ 0 & -1 & 1\end{array}\right)$,
(h) $\left(\begin{array}{rrrr}2 & 1 & 0 & 1 \\ 0 & 0 & 1 & 3 \\ 1 & 0 & 0 & -1 \\ 0 & 0 & -2 & -5\end{array}\right)$,
(i) $\left(\begin{array}{rrrr}1 & -2 & 1 & 1 \\ 2 & -3 & 3 & 0 \\ 3 & -7 & 2 & 4 \\ 0 & 2 & 1 & 1\end{array}\right)$.
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1 Linear Algebraic Systems