Problems:
1. Find all solutions of the equations using Gauss-Jordan elimination.
2. ¦ x + y = 1 ¦
¦2x - y = 5 ¦
¦3x + 4y = 2¦
3. ¦ x3 + x4 = 0¦
¦ x2 + x3 = 0¦
¦x1 + x2 = 0¦
¦x1 + x4 = 0¦
4. A father, when dying, gave to his sons 30 barrels, of which 10 were full of wine, 10 were half full, and the last 10 were empty. Divide the wine and flasks so that there will be equal division among the three sons of both wine and barrels. Find all the solutions of the problem. (from Alcuin)