2.4. EXERCISES 47

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

 .

Find solutions in Z7.

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

 .

in Z7.

15. Find the general solution in Z3 of the system whose augmented matrix is(2 1 0 11 0 1 2

).

16. Solve the system whose augmented matrix is1 0 2 1 1 20 1 0 1 2 11 2 0 0 1 01 0 1 0 2 2

in Z3

17. Find the general solution of the system whose augmented matrix is1 0 2 1 1 20 1 0 1 2 10 2 0 0 1 31 −1 2 2 2 0

 .

Find the solutions to this one in Z5.

18. Give the complete solution to the system of equations, 7x+ 14y+ 15z = 22, 2x+4y+3z = 5, and 3x+6y+10z = 13.

19. Give the complete solution to the system of equations, 3x− y+ 4z = 6, y+ 8z = 0,and −2x+ y =−4.

20. Give the complete solution to the system of equations, 9x− 2y+ 4z = −17, 13x−3y+6z =−25, and −2x− z = 3.

21. Give the complete solution to the system of equations, 65x+84y+16z = 546, 81x+105y+20z = 682, and 84x+110y+21z = 713.