| Date | Sec | Page | Questions |
|---|---|---|---|
| Mon 11 Jan | 1.1 | Intro to Matrices, Linear Systems | |
| Wed 13 Jan | 1.2 | Row Operations, Gaussian Elimination | |
| Fri 15 Jan | 1.3 | Matrix Add, Scalar Mult, Transpose, Identity, Multiply | |
| Mon 18 Jan | 1.4 | Matrix Inverse | |
| Wed 20 Jan | 1.5 | Calculating the Inverse | |
| HW1 | 1.1 | p. 6 | # 1, 4, 5, 7, 8 |
| 1.2 | p. 19 | # 2bdf, 4ac, 6bc, 7bc, 10, 14, 16, 17, 18 (no fractions), 23 (bonus: solve for arbitrary λ) | |
| 1.3 | p. 34 | # 2, 3, 4, 5, 13 | |
| Fri 22 Jan | 1.6-1.7 |
When is a System Solvable? Diagonal, Triangular, Symmetric Matrices | |
| Mon 25 Jan | 2.1 | Determinants via Cofactors | |
| Wed 27 Jan | 2.1-2.2 | Adjoint and Inverse, Cramer's Rule, Determinant via Gaussian Elimination | |
| HW2 | 1.3 | p. 37 | # 23, 29 |
| 1.4 | p. 49 | # 8, 12, 14, 16 (give an example), 21 | |
| 1.5 | p. 58 | # 6ac, 7abc, 8e, 9, 22 | |
| Fri 29 Jan | 2.3 (skip 2.4) | Properties of Determinants; Eigenvalues | |
| Mon 1 Feb | 3.1-3.2 | Eigenvalues; Geometry: Vectors, Dot Product | |
| Wed 3 Feb | 3.3-3.4 | Projections, Cross-Product, Lagrange's Identity | |
| HW3 | 1.6 | p. 66 | # 3, 17, 20 |
| 1.7 | p. 74 | # 16, 22, 24 (A=LU is called the "L-U decomposition"), 28 | |
| ch1 | p. 77 | # 15 (this is called interpolation), 16, 27 | |
| 2.1 | p. 94 | # 7, 9, 12, 23, 33 | |
| 2.2 | p.101 | # 5, 9, 13 | |
| ch2 | p.119 | # 10 | |
| Fri 5 Feb | 3.4 | Area of Parallelogram, Volume of a Parallelepiped | |
| Mon 8 Feb | 3.5 | Lines/Planes: vector forms, point-normal form | |
| Wed 10 Feb | 4.1-4.2 | Distance from point to plane; Euclidean n-space | |
| HW4 | 2.2 | p.103 | # 21 (for n x n; each add/mult counts as one op) |
| 2.3 | p.110 | # 5, 13, 23 (prove or show a counterexample!) | |
| 3.1 | p.130 | # 9, 19, 20 | |
| 3.2 | p.134 | # 4, 12 | |
| 3.3 | p.142 | # 3 (say why), 4, 11, 28 | |
| 3.4 | p.154 | # 18, 19 | |
| Fri 12 Feb | 4.2 | Properties of Inner Product; Linear Transforms in R3 | |
| Mon 15 Feb | 4.3 | Transforms: Scaling, Rotation, One-to-one | |
| Wed 17 Feb | -.- | Midterm 1 (ch1-§3.4) | |
| Fri 19 Feb | 4.4 | Visualizing Linear Transforms, Determinant, Eigenvalue | |
| Mon 22 Feb | (Independent Study Week; no class) | ||
| Wed 24 Feb | (Independent Study Week; no class) | ||
| Fri 26 Feb | (Independent Study Week; no class) | ||
| Mon 1 Mar | 4.4 | Space of Polynomials, Affine Transformations | |
| Wed 3 Mar | 4.4 | Polynomial Interpolation: Vandermonde vs. Newton | |
| HW5 | 3.4 | p.153 | # 4, 10, 30 |
| 3.5 | p.163 | # 11, 24, 33, 45 | |
| 4.1 | p.178 | # 6, 10, 16, 24, 26, 37 | |
| 4.2 | p.194 | # 7, 8, 17, 21, 32 | |
| Fri 5 Mar | 5.1 | Axioms of Vector Spaces | |
| Mon 8 Mar | 5.2 | Subspaces | |
| Wed 10 Mar | 5.3 | Linearly Independent Sets of Vectors | |
| HW6 | 4.3 | p.207 | # 6, 14, 16, 18 (see answers for 19), 22, 28 |
| 4.4 | p.217 | # 2, 3, 5, 8, 13, 14, 19 | |
| Fri 12 Mar | 5.4 | Vector Bases and Dimension of Space | |
| Mon 15 Mar | 5.5 | Column-Space, Row-Space, and Null-Space | |
| Wed 17 Mar | 5.6 | Rank + Nullity = # Columns | |
| HW7 | 5.1 | p.226 | # 6, 8, 14, 15, 26, 27, 31 |
| 5.2 | p.238 | # 2, 3, 6, 13, 21, 25 | |
| 5.3 | p.248 | # 2, 8, 14, 16, 21 | |
| Fri 19 Mar | 6.1 | Inner Product Spaces | |
| Mon 22 Mar | 6.2 | Norm, Distance, Angle, Orthogonality | |
| Wed 24 Mar | 6.3 | Orthonormal Bases, Gram-Schmidt Process | |
| HW8 | 5.4 | p.263 | # 2, 4, 5, 10, 18, 24, 32 |
| 5.5 | p.276 | # 6(acd), 8(acd), 12, 15 | |
| 5.6 | p.288 | # 2(acd), 12 | |
| ch5 | p.290 | # 2, 4, 8, 12 (hint: think about a basis for all 2x2 matrices) | |
| Fri 26 Mar | 6.4 | QR Decomposition, Least Squares Approximation | |
| Mon 29 Mar | 3.5-5.6 | Review §3.5-5.6 | |
| Wed 31 Mar | 3.5-5.6 | Midterm 2 | |
| Fri 2 Apr | (Good Friday; no class) | ||
| Mon 5 Apr | (Easter Monday; no class) | ||
| Wed 7 Apr | 6.4-6.6 | Orthogonal Matrices, Least Squares Approximation | |
| HW9 | 6.1 | p.304 | # 6, 10, 18, 28(ab) |
| 6.2 | p.315 | # 6, 18(ac), 31, 34 | |
| 6.3 | p.329 | # 16, 24(acd) | |
| Fri 9 Apr | 7.1-7.2 | Eigenvectors and Diagonalization | |
| Mon 12 Apr | 7.2-7.3 | Orthogonal Diagonalization | |
| Wed 14 Apr | 7.3 | Diagonalization | |
| HW10 | 6.1 | p.306 | # 24 |
| 6.2 | p.315 | # 16, 38 | |
| 6.3 | p.329 | # 18, 29, 30 | |
| 6.4 | p.339 | # 3(ad), 10, 18 | |
| 6.6 | p.354 | # 2, 4, 6, 20 | |
| Fri 16 Apr | ch1-7 | Semester Review | |
| Tue 27 Apr | Final Exam: 9am-12pm (note: 3hrs given for math finals) | ||