Problem Set I, for Thursday, January 17 (at 11:00).
Section 1.1, page 6, Exercises 6 and 8.
Section 1.2, page 12, Exercises 16 and 35.
Section 1.3, page 18, Exercises 22 and 26.
Solutions are posted (in pdf format).
Problem Set II, for Thursday, January 24 (at 11:00).
Section 2.1, page 29, Exercises 12 and 20.
Section 2.2, page 35, Exercises 2 and 10.
Section 2.3, page 39, Exercises 8 and 9.
Suggestion for #9(b): Multiply the first equation in part (a) by b_1.
Solutions are posted (in pdf format).
Problem Set III, for Monday, January 28 (at 11:00).
Section 3.1, page 50, Exercises 16 and 31. (Cf. #9.)
Section 3.2, page 62, Exercises 22 and 32.
Solutions are posted (in pdf format).
Problem Set IV, for Thursday, February 7 (at 11:00).
Section 3.3, page 76, Exercises 7 (see the hint on page 558), 9, and 29.
Note that #28 is a special case of #29, where T = {0}.
The K in #28 stands for kernel; this will be an important word later.
Section 4.1, page 88, Exercises 6, 12, and 13.
Solutions are posted (in pdf format).
Problem Set V, for Thursday, February 14 (at 11:00).
Section 4.2, page 93, Exercises 5(b), 6(b), and 14.
(Everyone should do a calculation like #5 and #6 once.)
Section 4.3, page 98, Exercises 9(b), 12, and 23.
(See the hint for #23 on page 560.)
Solutions are posted (in pdf format).
Problem Set VI, for Thursday, February 21 (at 11:00).
Section 4.4, page 104, Exercises 2(b), 11, and 14(a).
In #14, assume r and s are different.
Section 4.5, page 113, Exercise 1(b).
Explain why the factors you obtain are irreducible.
Section 4.6, page 117, Exercises 2(c) and 3(b).
Solutions are posted (in pdf format).
Problem Set VII, for Thursday, February 28 (at 11:00).
Section 5.1, page 122, Exercises 6, 7, and 8.
For #6, it might help to look at #3 on page 132, and its answer
on page 562. For #7, see #3 (and its answer on page 561)
and #4.
Section 5.2, page 128, Exercises 6, 8, and 10.
Solutions are posted (in pdf format).
Problem Set VIII, for Thursday, March 6 (at 11:00).
Section 5.3, page 132, Exercises 2(b), and 3.
Exercise 2(a) was in Problem Set III.
For #3, see the answer on page 562.
Solutions are posted (in pdf format).
Problem Set IX, for Thursday, March 13 (at 11:00).
Section 6.1, page 141, Exercises 8, 32, and 38.
Section 6.2, page 151, Exercises 4, 14, and 25(b).
Section 6.3, page 157, Exercises 8 and 10.
Solutions are posted (in pdf format).