| Monday, 1/6 | Intro to the course. Systems of linear equations (Section 1.1) and solving them via row operations on matrices. |
| Wednesday, 1/8 | Matrices, Gauss-Jordan elimination (Section 1.2). Read: Section 1.2. |
| Friday, 1/10 | The number of solutions to a linear system; matrix algebra (Section 1.3). A few words on linear transformations (Section 2.1) Read: Section 1.3. HW #1 due: Section 1.1, #6, 7, 15, 17, 25, 32, 46. Section 1.2, #4, 6, 7, 22, 26, 27, 36, 69, 72. |
| Monday, 1/13 | Linear Transformations (Section 2.1) Read: Section 2.1 |
| Wednesday, 1/15 | Linear Transformations in Geometry (Section 2.2). Read: Section 2.2, start on 2.3 HW #2 due: Section 1.3, #4, 18, 23, 24, 25, 26, 28, 47, 58. Section 2.1, #5, 6, 7, 21, 31, 32, 33. |
| Friday, 1/17 | More on projections and shears (Section 2.2). Matrix multiplication (Section 2.3). Read: review 2.2, read 2.3 |
| Monday, 1/20 | More matrix multiplication. Inverses (Section 2.4). Read: Review 2.3, read 2.4. HW #3 due: Section 2.2, #4, 6, 8, 9, 10, 11, 14, 19, 20, 27, 28. Section 2.3, #1, 3, 5, 7, 9, 18, 36, 37, 44, 46. |
| Wednesday, 1/22 | More on inverses. The image and kernel of a linear transformation (3.1) Read: Section 3.1 |
| Friday, 1/24 | More on image and kernel. A bit on subspaces. Read: review Section 3.1. HW #4 due: Section 2.4, #2, 4, 6, 10, 13, 32, 34, 35, 41, 53, 67, 68, 71, 72. Section 3.1, #6, 7, 12, 24, 39, 40. |
| Monday, 1/27 | Subspaces and bases. Read: Section 3.2 |
| Wednesday, 1/29 | Linear independence. HW #5 due: Section 3.1, #14, 15, 18, 22, 30, 49, 51. Section 3.2, #2, 3, 6. |
| Friday, 1/31 | More on linear independence. A bit on dimension. Read: Re-read Section 3.2 on linear independence. Read first part of Section 3.3. HW #6 due: Section 3.2, #16, 24, 36, 37, 39, 43. |
| Monday, 2/3 | Review |
| Wednesday, 2/5 | Midterm 1 |
| Friday, 2/7 | Dimension. Read: Section 3.3 |
| Monday, 2/10 | Mid-term break |
| Wednesday, 2/12 | Final thoughts on dimension. Finding bases for the kernel and image of a matrix. Read: Pages 136-142 (in Section 3.3). HW #7 due: Section 3.3, #9, 20 (to find a basis for the kernel, compute the kernel as the span of some vectors, then check that those vectors are linearly independent), 27, 28, 29, 62, 63, 64, 80 (you'll want to use Theorem 3.3.4 for numbers 62-64. For number 80, think about Theorem 3.3.1). |
| Friday, 2/14 | The rank-nullity theorem. Linear Spaces. Read: Section 4.1 through Definition 4.1.3, and also Summary 4.1.6. |
| Monday, 2/17 | Linear Spaces and their linear transformations (Sections 4.1 and 4.2). Read: Pages 174-175 and Section 4.2 through Definition 4.2.2. HW #8 due: Section 3.3, #21, 22, 25, 36, 37, 38, 39. Section 4.1, #1-6, 9, 10, 27, 28, 47, 48. |
| Wednesday, 2/19 | Coordinates and the matrix of a linear transformation (Corresponds to parts of Section 4.1 and 4.3) Read: Pages 172-173 and pages 187-190. |
| Friday, 2/21 | More on Coordinates and the matrix of a linear transformation. HW #9 due: Section 4.2, #1-5, 22, 23, 26, 27, 45, 48, 53, 63. Section 4.3, #20-26. |
| Monday, 2/24 | Change of Basis (Section 4.3). A few words on determinants (Section 6.1) Read: pages 191-194. |
| Wednesday, 2/26 | Determinants. Read: Section 6.2 (you can ignore the stuff about "patterns") HW #10 due: Section 4.3, #13, 14, 20, 21, 35, 36, 37, 44, 46, 48. |
| Friday, 2/28 | A bit more on determinants. Review. |
| Monday, 3/3 | Midterm 2 |
| Wednesday, 3/5 | Eigenvectors and Eigenvalues. Read: Section 7.1, first part of 7.2. |
| Friday, 3/7 | More eigenvectors and eigenvalues. Read: rest of 7.2, section 7.3. |
| Monday, 3/10 | HW #11 due: Section 6.2, #6, 8, 9, 17, 30, 39. Section 7.2, #3, 9, 13, 15, 18. Section 7.3, #3, 9, 11, 14, 18, 42, 48. |
| Wednesday, 3/12 | Projects due. |
| Monday, 3/17 | Final Exam, 8:30-11:00 am |