exo7 1171

Mettre sous forme matricielle et résoudre les systèmes suivants.

1

{2x+y+z=33x−y−2z=0x+y−z=−2x+2y+z=1\left\{\begin{array}{rcl}2x+y+z&=&3\\3x-y-2z&=&0\\ x+y-z&=&-2\\x+2y+z&=&1\end{array}\right.

2

{x+y+z+t=1x−y+2z−3t=22x+4z+4t=32x+2y+3z+8t=25x+3y+9z+19t=6\left\{\begin{array}{rcl}x+y+z+t&=&1\\x-y+2z-3t&=&2\\ 2x+4z+4t&=&3\\2x+2y+3z+8t&=&2\\5x+3y+9z+19t&=&6\end{array}\right.

3

{2x+y+z+t=1x+2y+3z+4t=23x−y−3z+2t=55y+9z−t=−6\left\{\begin{array}{rcl}2x+y+z+t&=&1\\x+2y+3z+4t&=&2\\ 3x-y-3z+2t&=&5\\5y+9z-t&=&-6\end{array}\right.

4

{x−y+z+t=52x+3y+4z+5t=83x+y−z+t=7\left\{\begin{array}{rcl}x-y+z+t&=&5\\2x+3y+4z+5t&=&8\\ 3x+y-z+t&=&7\end{array}\right.

5

{x+2y+3z=02x+3y−z=03x+y+2z=0\left\{\begin{array}{rcl}x+2y+3z&=&0\\2x+3y-z&=&0\\ 3x+y+2z&=&0\end{array}\right.

Exercice uO3B

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