4.3. EXERCISES 75

18. Choose h and k such that the augmented matrix shown has one solution. Then chooseh and k such that the system has no solutions. Finally, choose h and k such that thesystem has infinitely many solutions.(

1 2 | 22 h | k

).

19. Determine if the system is consistent. If so, is the solution unique?

x+2y+ z−w = 2x− y+ z+w = 1

2x+ y− z = 14x+2y+ z = 5

20. Determine if the system is consistent. If so, is the solution unique?

x+2y+ z−w = 2x− y+ z+w = 0

2x+ y− z = 14x+2y+ z = 3

21. Find the general solution of the system whose augmented matrix is 1 2 0 | 21 3 4 | 21 0 2 | 1

 .

22. Find the general solution of the system whose augmented matrix is 1 2 0 | 22 0 1 | 13 2 1 | 3

 .

23. Find the general solution of the system whose augmented matrix is(1 1 0 | 11 0 4 | 2

).

24. Find the general solution of the system whose augmented matrix is1 0 2 1 1 | 20 1 0 1 2 | 11 2 0 0 1 | 31 0 1 0 2 | 2

 .