Math 224 Linear Algebra I
Tuesday and Thursday 9:4011:00am
Hayes Hall 311
Textbook
Linear Algebra, A Modern Introduction,
Third Edition, by David Poole.
Office
Hours (Hayes 309A)
Monday 2:103:00
Tuesday 3:104:00
Wednesday 3:104:00
Thursday 1:103:00
Dropin
Tutoring with Margo (Tomsich 207)
Monday 7:309:00
Wednesday 7:309:00
Note that the material is slightly shifted – similarity and diagonalization do not appear on this exam but will appear
on our ODK 2. This exam is intended to give you extra practice problems; it is
not a sample exam.
Homework
Assignment 
Problems 
Due Date 
1 
Exercises 1.1: #1c, 2c, 3d, 4d, 5bd, 6, 10,
12, 16, 17, 21, 23, 24 
Tuesday, 8/30 
2 
Exercises 1.2: #4, 10, 16, 17b, 20, 26, 31, 34, 39, 41, 43 
Thursday, 9/1 
3 
Exercises 1.2: 49, 59, 62, 63 Exercises 1.3: 2, 6, 9, 14, 22,
24, 28, 41, 43, 48bd Exercises 1.4: 21, 25, 28, 32,
35 
Tuesday, 9/6 
4 
Exercises 2.1: 3, 4, 6, 10, 13, 17,
21, 30, 35, 40, 41 Exercises 2.2: [1, 3, 4, 6, 8] – just
determine if the matrix is in row echelon form (don't worry about reduced row
echelon form), 16 
Thursday, 9/8 
5 
Exercises 2.2: [1, 35] – now both
REF and RREF, 11, 13, 18, 21 (note that the row
operation is okay, but it is not elementary), 31, 32, 35, 37, 41, 46, 47, 49, 58,
59 
Tuesday, 9/13 
6 
Exercises 2.3: 4, 5, 11, 16, 18, 20,
25, 28, 35, 38, 42 
Thursday, 9/15 
7 
Problem 6 from inclass worksheet. Exercises 2.4: 1, 4, 8, 11, 16, 18,
20, 26, 38, 41, 42, 45, 47 We'll talk about finite linear games
in class on Tuesday. 
Tuesday, 9/20 
8 
Tuesday, 9/27 

9 
Exercises 3.1: 1, 6, 7, 8, 13, 18, 19, 21, 23, 25, 30, 33, 35 You can use Maple to check your answers, but you should do these
problems by hand (the one exception is #35a, for which you may use Maple.) 
Tuesday, 9/27 
10 
Exercises 3.2: 4, 6, 10, 16, 19, 26, 3638, 40 Exercises 3.3: 16 
Thursday, 9/29 
11 
Exercises 3.3: 2, 3, 12, 19, 23, 40, 44, 47, 48, 53, 61, 65, 69 Study for ODK 1! 
Tuesday, 10/4 

Survey for extra credit 
Tuesday, 10/11 
12 
Exercises
3.5: 3, 810, 12, 1416 
Thursday, 10/13 
13 
Remember
that you can use Maple to row reduce. If you do so, write out the matrix you
started with and its row reduced form and mention that you used Maple. Exercises 3.5: 19, 23, 30, 32, 37, 42, 47, 52, 55, 58, 59b, 62 Write up the proof of Thm 3.28(a) in
your own words. Read the entire section carefully; make sure you understand the
proof of Thm 3.29. 
Tuesday, 10/18 
14 
Exercises 3.6: 2, 4, 8, 12, 16, 18, 31, 44, 45, 54 
Thursday, 10/20 
15 
Exercises 3.6: 21, 22, 39, 40, 42 Hint for 42(b): Show that the matrix A for the projection is not
invertible by showing that there is a nonzero vector x = (AI)e_{k} in the null space
of A. Why does this show A is not invertible? Work on your project! 
Tuesday, 10/25 
16 
Exercises 4.1: 5, 14, 16, 2022, 23, 26, 28, 32, 35, 37 Work on your project! 
Thursday, 10/27 
17 
Exercises 4.2: 8, 15, 17, 20, 24, 27, 29, 33, 42, 49, 54, 60, 64 You
can use Maple to check your answers but all computations should be carried
out by hand for this assignment. 
Thursday, 11/5 

Project! 
Tuesday, 11/3 
18 
Exercises 4.3: 7, 19, 21, 22, 24 The use of Maple is okay for determinant, matrix multiplication,
and row reduction purposes (for both the worksheets and the book work). 
Thursday, 11/5 
19 
Exercises 4.3: 17, 18, 31 (ignore the
hint and use your new knowledge), 34, 36, 38 Exercises 4.4: 4, 6, 11,
14, 20, 29, 30, 37, 41 The use of Maple is okay. As usual, state when you use it as
well as what you found. 
Tuesday, 11/8 
20 
Exercises 5.1: 2, 6, 7, 10, 13, 17, 19, 27, 28, 30, 36 Hadamard Matrices Worksheet 
Tuesday, 11/15 
21 
Exercises 5.2: 6, 7, 9, 13, 16, 22, 25, 27, 28 Find the Error Worksheet 
Tuesday, 11/29 
22 
Exercises 5.3: 1, 6, 8,
10, 12, 16, 19 Form
project groups and choose topic. 
Thursday, 12/1 

Work on
projects! 

23 
Exercises 5.4: 2, 6,
11, 13, 15, 20, 24, 25 
Final exam
day: Tuesday,
12/13 at 1:30pm 
24 
Exercises 3.7: 80, 81,
84, 85, 88, 92 Exercises 5.5: 2, 3, 7,
11, 15, 18, 22 Note that the generator
matrix for the dual code is P^{T}, and the parity check
matrix for the dual code is G^{T}. (I accidentally switched
those in class.) If you’re curious, the
pictures of Mars, Jupiter, and Saturn sent using linear codes are on page
543. If you choose, you can turn
in the last two assignments by Thursday at 4pm. Note, however, that the best
way to learn the material is to do the assignment, and the material is fair
game for the exam. 
Tuesday,
12/13 at 1:30pm 