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\(\begin{array}{l}
1)\\
\kern26pt A = \left(\matrix{2&-4&3&1&0\\1&-2&1&-4&2\\0&1&-1&3&1\\1&-7&4&-4&5} \right)\\
\xrightarrow{\begin{array}{l} r_2 - \tfrac12r_1 \to r_2\\r_4 - \tfrac12r_1 \to r_4 \end{array}}
\left(\matrix{2&-4&3&1&0\\0&0&-\dfrac12&-\dfrac92&2\\0&1&-1&3&1\\0&-5&\dfrac52&-\dfrac92&5} \right)\\
\xrightarrow{\quad r_3 \leftrightarrow r_2\quad}
\left(\matrix{2&-4&3&1&0\\0&1&-1&3&1\\0&0&-\dfrac12&-\dfrac92&2\\0&-5&\dfrac52&-\dfrac92&5} \right)\\
\xrightarrow{\ r_4 + 5r_2 \to r_4\ }
\left(\matrix{2&-4&3&1&0\\0&1&-1&3&1\\0&0&-\dfrac12&-\dfrac92&2\\0&0&-\dfrac52&\dfrac{21}{2}&10} \right)\\
\xrightarrow{\ r_4 - 5r_3 \to r_4\ }
\left(\matrix{2&-4&3&1&0\\0&1&-1&3&1\\0&0&-\dfrac12&-\dfrac92&2\\0&0&0&33&0} \right)\\
2)\\
\kern30pt A = \left(\matrix{0&2&-4\\-1&-4&5\\3&1&7\\0&5&-10\\2&3&0} \right)\\
\xrightarrow{\kern15pt \begin{array}{l}r_4 \leftrightarrow r_2\\r_3 \leftrightarrow r_1\end{array}\kern15pt }\left(\matrix{-1&-4&5\\0&5&-10\\0&2&-4\\3&1&7\\2&3&0} \right)\\
\xrightarrow{\ \ \begin{array}{l}r_4 + 3r_1 \to r_4\\r_5 + 2r_1 \to r_5 \end{array}\ \ }\left(\matrix{-1&-4&5\\0&5&-10\\0&2&-4\\0&-11&22\\0&-5&10} \right)\\
\xrightarrow{\begin{array}{l}r_3 -\tfrac25r_2 \to r_3\\r_4 + \tfrac{11}{5}r_2 \to r_4\\r_5 + r_2 \to r_5 \end{array}}\left(\matrix{-1&-4&5\\0&5&-10\\0&0&0\\0&0&0\\0&0&0} \right)\\
\end{array}\)
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