How to use the suggested homework assignments effectively:
Try the problems before we discuss the section in class.
If completely stuck or very uncertain, try a similar ebedded problem with
an answer in the back if possible. If still stuck or uncertain, add
the problem to a list of questions to ask in class or office hours.
As a final step, check your solution against those that will be on reserve
in the library.
Even though these will not be graded, write up complete, organized
final solutions as if they were. This will likely improve your performance
on quizzes and exams and will be helpful to refer back to when studying
for these.
| Homework 1
(1.1-1.4) |
Section 1.10: 4, 8, 12, 16, 18, 22, 24, 54, 58
Also prove the following: 1. For any vectors a and v and any scalar c, <a,cv>=c<a,v>. 2. <x,x> is greater than or equal to 0 and equals 0 if and only if x=0. 3. For any two matrices A and B of the same size and any scalars c and d, c(A+B)=cA+cB, and (c+d)A=cA+dA. 4. If A is any m by n matrix and e_i is the vector with a 1 in the i-th position and 0 in all other positions, then Ae_i=A^i (the i-th column of A). |
| Homework 2
(1.5-1.7) |
Section 1.10: 14, 29, 42, 44, 47, 50-52, 56, 68, 74, 76, 82,
84, 86
(Suggested: 34, 36, 38, 65, 69, 71) Also prove the following: 5. The product of two upper triangular matrices is upper triangular. 6. The transpose of the product of n matrices is the product of the transposes in the opposite order. |
| Homework 3
(1.8-2.1) |
Section 1.10: 89, 90, 96, 104, 108, 110
Section 2.9: 1, 4, 6, 9, 11, 12, 20 |
| Homework 4
(2.2-2.3) |
Section 2.9: 14, 17, 23, 26a, 29, 32, 34, 36a,d, 37b, 38, 46,
51a,b,c
Also, include the basis parts of 1 and 6, and 11b from the previous assignment. |
| Homework 5
(2.4-2.7) |
Section 2.9: 41, 51d,e, 58, 59, 66, 73, 76, 79, 84, 86, 92, 95, 98, 101, 104, 108, 109 |
| Homework 6
(3.1-3.2) |
Section 3.7: 3, 5, 6, 11, 13, 16 (use the inner product given above on p. 225), 21, 22, 32, 34, 37, 38 |
| Homework 7
(3.3-3.5) |
Section 3.7: 1, 12, 18 (use the inner product given above on p. 225), 39, 43a,b,c (explain c), 47, 52, 59, 64 |
| Homework 8
(4.1-4.3) |
Section 4.6: Do 3, 6 by hand, Do 11, 14 by Maple, 16-18, 20,
24, 27, 31, 32, 42, 45
Prove that if A is diagonalizable and A is similar to B, then B is diagonalizable. |
| Homework 9
(5.1-5.2) |
Section 4.6: 8 (by hand), 29, 37, 39
Section 5.6: 8-10 (individual steps may be done in Maple), 21, 22, 25a,c |
This is the schedule of sections that will be discussed
in class with suggested embedded exercises to practice before class.
Updates will be announced in class and/or posted on the web page.
| Monday | Wednesday | Friday |
| 1/14
1.1 - One Equation, n Unknowns Sugg: 1.1 #1 |
1/16
1.2 - Matrices, Systems of Eq'ns Sugg: 1.2 #2-5 |
1/18 Quiz 1 on 1.1, 1.2
1.2/1.3 - Solving Reduced Systems Sugg: 1.3 #2, 3, 5, 6, 8 |
| 1/21 No Class | 1/23
1.3 - Solving Reduced Systems Sugg: 1.3 #2, 3, 5, 6, 8 |
1/25
1.4 - Gaussian Elimination Sugg: 1.4 #2-4, 7-9 |
| 1/28 Quiz 2 up to 1.4
1.4/1.5 - Elementary Matrices Sugg: 1.5 #1-6, 8 |
1/30
1.5 - Elementary Matrices Sugg: 1.5 #1-6, 8 |
2/1
1.5 - Elementary Matrices Sugg: 1.6 #1-4, 6, 7, 9, 10 |
| 2/4
1.6 - Inverses and Transposes Sugg: 1.7 #1-3, 5, 10-12 |
2/6 Quiz 3 up to 1.6
1.6 - Inverses and Transposes Sugg: 1.8 #1-2 |
2/8
1.7 - Determinants Sugg: 1.9 #1, 2, 4, 5 |
| 2/11
1.7 - Determinants Sugg: 2.1 #1-5 |
2/13 Quiz 4 up to 1.7
1.8 - Computational Notes Sugg: 2.1 #1-5 |
2/15
2.1 - Vector Spaces, Subspaces Sugg: 2.1 #1-5 |
| 2/18 No Class | 2/20
2.1 - Vector Spaces, Subspaces Sugg: 2.1 #1-5 |
2/22 Quiz 5 on 1.8, vector space
properties
2.2 - Span, Linear Independence Sugg: 2.2 #4, 6, 7, 8 |
| 2/25
2.2 - Span, Linear Independence Sugg: 2.2 #1, 2a,b,d, 3, 4, 6, 7, 8 |
2/27
2.3 - Linear Transformations Sugg: 2.3 #1, 3, 4 |
3/1
Exam 1 on 1.1-2.1 |
| 3/4
2.3 - Linear Transf. Sugg: 2.3 #1, 3, 4 |
3/6
2.4 - Isomorphism, Dimension Sugg: 2.4 #1-3, 6 |
3/8
2.5 - Linear Transf., Subspaces 2.5 #2, 3, 6, 7, 8, 10 |
| 3/11
2.5 - Linear Transf., Subspaces 2.5 #2, 3, 6, 7, 8, 10 |
3/13
2.6 - Subspace Construction Sugg: 2.6 #2-4 |
3/15
2.7 - Linear Transf., Matrices Sugg: 2.7 #4, 5, 7-9, 11-13 |
| 3/25
2.7 - Linear Transf., Matrices Sugg: 2.7 #4, 5, 7-9, 11-13 |
3/27
3.1 - Orthogonalization, QR Sugg: 3.1 #1, 2, 4-6 |
3/29
3.1/3.2- Orthogonal Subspaces Sugg: 3.2 #1, 3, 4 |
| 4/1
3.2 - Orthogonal Subspaces Sugg: 3.2 #1, 3, 4 |
4/3
3.3 - Orthogonal Projections Sugg: 3.3 #2, 3, 4 |
4/5
3.3 - Orthogonal Projections Sugg: 3.3 #2, 3, 4 |
| 4/8
3.4 - Least Squares Sugg: 3.4 #2 |
4/10
3.4/3.5 - Data Fitting Sugg: 3.5 #1, 3, 4-6 |
4/12
3.5 - Data Fitting Sugg: 3.5 #1, 3, 4-6 |
| 4/15
4.1 - Eigenvalues, Eigenvectors |
4/17
Conjectures Sugg: 4.1 #3-5 |
4/19
Exam 2 2.3-3.5 |
| 4/22
4.1/4.2 - Diagonalizability Sugg: 4.1 #3-5; 4.2 #1, 3, 4, 6 |
4/24
4.2 - Diagonalizability Sugg: 4.2 #1, 3, 4, 6 |
4/26
4.3 - Complex Vectors, Matrices Sugg: 4.3 #1, 2, 4-9 |
| 4/29
5.1 - Complex Vector Spaces Sugg: 5.1 #2, 5 |
5/1
5.1/5.2 - Spectral Theorem Sugg: 5.2 #1, 3, 4 |
5/3
5.2 - Spectral Theorem Sugg: 5.2 #1, 3, 4 |
| 5/6
4.5 - Applications to DEs |
5/8
Applications |
5/10
Review |