This is the schedule of sections that will be discussed in class with
suggested embedded exercises to practice before class and due dates of
homework assignments.
Check back for updates.
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| 1/16 1.1 - One Equation in n Unknowns
Sugg: 1.1 #1 |
1/18 1.2 - Matrices and Systems of Equations
1.3 - Solving Systems in Reduced Form Sugg: 1.2 #2-5, 1.3 #2, 3, 5, 6, 8 |
| 1/23 1.4 - Gaussian Elimination
Sugg: 1.4 #2-4, 7-9 |
1/25 1.5 - Elementary Matrices
Sugg: 1.5 #1-6, 8 Homework #1 Due |
| 1/30 1.6 - Inverses and Transposes
Sugg: 1.6 #1-4, 6, 7, 9, 10 |
2/1 1.7 - Determinants
Sugg: 1.7 #1-3, 5, 10-12 |
| 2/6 1.7, 1.8 - Computational Notes
Sugg: 1.8 #1-2 |
2/8 1.8, 1.9 - Applications
Sugg: 1.9 #1, 2, 4, 5 Homework #2 Due |
| 2/13 2.1 - Vector Spaces and Subspaces
Sugg: 2.1 #1-5 |
2/15 2.1 - Subspaces
Sugg: 2.2 #1, 2a,b,d, 3 |
| 2/20 2.2 - Span and Linear Independence
Sugg: 2.2 #4, 6, 7, 8 Homework #3 Due |
2/22 2.2 - Basis and Dimension
Sugg: 2.2 #4, 6, 7, 8 Exam 1 Out |
| 2/27 2.3 - Linear Transformations
Sugg: 2.3 #1, 3, 4 Exam 1 Due |
3/1 |
| 3/6 2.4, 2.5 - Isomorphism, Linear Transformations
and Subspaces
Sugg: 2.4 #1-3, 6; 2.5 #2, 3, 6, 7, 8, 10 Homework #4 Due |
3/8 2.5, 2.6 - Subspace Construction
Sugg: 2.5 #2, 3, 6, 7, 8, 10, 2.6 #2-4 |
| 3/13 2.7 - Linear Transformations and Matrices
Sugg: 2.7 #4, 5, 7-9, 11-13 |
3/15 No class (in exchange for the take-home exams)
Feel free to use the class time to meet in groups to discuss material or homework problems together. |
| 3/27 2.7 - Linear Transformations and Matrices
Sugg: 2.7 #4, 5, 7-9, 11-13 |
3/29 3.1 - Orthogonalization and QR Decomposition
Sugg: 3.1 #1, 2, 4-6 Homework #5 Due |
| 4/3 3.2 - Orthogonal Subspaces
Sugg: 3.2 #1, 3, 4 |
4/3 3.3 - Orthogonal Projections
Sugg: 3.3 #2, 3, 4 |
| 4/10 3.3, 3.4 - Least Squares
Sugg: 3.3 #2, 3, 4 3.4 #2 Homework #6 Due |
4/12 3.5 - Data Fitting
Sugg: 3.5 #1, 3, 4-6 Exam 2 Out |
| 4/17 4.1 - Eigenvalues and Eigenvectors
Exam 2 Due |
4/19 Conjectures
Sugg: 4.1 #3-5 MEET IN GARRISON 713 COMPUTER LAB |
| 4/24 4.2 - Diagonalizability
Sugg: 4.2 #1, 3, 4, 6 Homework #7 Due |
4/26 4.3 - Complex Vectors and Matrices
Sugg: 4.3 #1, 2, 4-9 |
| 5/1 5.1 Complex Vector Spaces
Sugg: 5.1 #2, 5 |
5/3 5.2 Spectral Theorem
Sugg: 5.2 #1, 3, 4 Homework #8 Due |
| 5/8 4.5 - Applications to Differential Equations
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5/10 Applications
Homework #9 Due |
Here are the homework assignments.
| Homework 1
(1.1-1.4) Due Thurs. 1/25 |
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) Due Thurs. 2/8 |
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) Due Tues. 2/20 |
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) Due Tues. 3/6 |
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) Due Thurs. 3/29 |
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) Due Tues. 4/10 |
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) Due Tues. 4/24 |
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) Due Thurs. 5/3 |
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) Due Thurs. 5/10 |
Last Homework Assignment:
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 |