Résoudre les systèmes linéaires suivants :
\[(S_1) \left \{ \begin{array}{ccccccc} x & - & y & + & z & = & 1 \\ 2x & + & y & - & z & = & 2 \\ x & - & 2y & + & 3z & = & 0 \end{array} \right. ~~~~~~ (S_2) \left \{ \begin{array}{ccccccc} 2x & + & 3y & + & z & = & 4 \\ -x & + & y & + & 2z & = & 3 \\ 7x & + & 3y & - & 5z & = & 2 \end{array} \right.\]
\[(S_3) \left \{ \begin{array}{ccccccc} & & y & - & z & = & 1 \\ 2x & + & y & + & z & = & 3 \\ x & & & + & z & = & 1 \end{array} \right. ~~~~~~ (S_4) \left \{ \begin{array}{ccccccc} 2x& - & y & + & z & = & 3 \\ x & & & + & 2z & = & -1 \\ x & - & y & - & z & = & 2 \end{array} \right.\]
\[(S_5) \left \{ \begin{array}{ccccccccc} -3x & + & y & + & z & - &t &=&0 \\ x & - & 3y & + & z & + & t & = & 0\\ x & + & y & - & 3z & + & t & = & 0 \\ x & + & y & + & z &-& 3t &=& 0 \end{array} \right. ~~~~~ (S_6) \left \{ \begin{array}{ccccccccc} -x & + & 3y & & &- & t & = & 0 \\ 2x & - & y & + & 2z & + & 2t &=& 0\\ && 5y &+& 2z & & &=& 0\\ x &+& 2y & + &2z & +& t &=& 0 \end{array} \right.\]