(a) $A\text{}\to \text{}{A}^T$

Take the transpose of the matrix $A$:

${\left(\begin{array}{rrrr}-3& \phantom{-}0& \phantom{-}1& \phantom{-}3\\ \phantom{-}0& \phantom{-}3& \phantom{-}3& \phantom{-}3\\ \phantom{-}1& \phantom{-}1& \phantom{-}4& \phantom{-}3\\ \phantom{-}2& -4& -4& -3\end{array}\right)}^T=\left(\begin{array}{rrrr}-3& 0& 1& \phantom{-}2\\ \phantom{-}0& 3& 1& -4\\ \phantom{-}1& 3& 4& -4\\ \phantom{-}3& 3& 3& -3\end{array}\right)$

(b) $R_1\text{}\leftrightarrow \text{}{R}_4$

Swap the first and fourth rows:

$\left(\begin{array}{rrrr}\phantom{-}3& 3& 3& -3\\ \phantom{-}0& 3& 1& -4\\ \phantom{-}1& 3& 4& -4\\ -3& 0& 1& \phantom{-}2\end{array}\right)$

(c) $R_2\text{}\to \text{}2R_3-2R_2$

Replace the second row with the sum of $2$ times the third row and $-2$ times the second row:

$\left(\begin{array}{rrrr}\phantom{-}3& 3& 3& -3\\ \phantom{-}2& 0& 6& \phantom{-}0\\ \phantom{-}1& 3& 4& -4\\ -3& 0& 1& \phantom{-}2\end{array}\right)$

(d) $C_4\text{}\to \text{}-3C_4-4C_1$

Replace the fourth column with the sum of $-3$ times the fourth column and $-4$ times the first column:

$\left(\begin{array}{rrrr}\phantom{-}3& 3& 3& -3\\ \phantom{-}2& 0& 6& -8\\ \phantom{-}1& 3& 4& \phantom{-}8\\ -3& 0& 1& \phantom{-}6\end{array}\right)$

(e) $C_3\text{}\to \text{}-9C_3$

Scale the third column by a factor of $-9$:

$\left(\begin{array}{rrrr}\phantom{-}3& 3& -27& -3\\ \phantom{-}2& 0& -54& -8\\ \phantom{-}1& 3& -36& \phantom{-}8\\ -3& 0& \phantom{0}-9& \phantom{-}6\end{array}\right)$