$$ \begin{array}[t]{rrrrr} 2x_1&-5x_2&+4x_3&+3x_4&=0,\\ 3x_1&-4x_2&+7x_3&+5x_4&=0,\\ 4x_1&-9x_2&+8x_3&+5x_4&=0,\\ -3x_1&+2x_2&-5x_3&+3x_4&=0. \end{array} $$
$$ \left(\begin{array}{cccc} 3&2&1&2\\ 7&5&2&5\\ 0&0&9&4\\ 0&0&11&5 \end{array}\right) $$
$$ \left|\begin{array}{cccc} 0&1&2&3\\ 1&0&1&2\\ 2&1&0&1\\ 3&2&1&0 \end{array}\right| $$
$$ \left(\begin{array}{rrrrr} -5&3&-4&0&3\\ 4&0&0&-1&3\\ -3&1&0&2&0\\ 2&0&0&-3&0 \end{array}\right) $$