MTH 210: Intro to Linear Algebra
University of Miami, Spring 2023
Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: Tues/Thurs 10-11, or by appointment
Class Time and Location: 12:30-1:45 Tuesdays and Thursdays in Whitten LC 194.
Course syllabus can be found here.
Text: Introduction to Linear Algebra (5th ed) by Gilbert Strang
The sections listed below (for example § 1.1) refer to the relevant section in Strang's book.
The symbol § used below means "Section".
Homework Assignments
| Assignment |
Due Date |
| Homework 1: PDF
| 1/26/23 |
| Homework 2: PDF
| 2/9/23 |
| Homework 3: PDF
| 2/21/23 |
| Homework 4: PDF
| 3/9/23 |
| Homework 5: PDF
| 3/23/23 |
| Homework 6: PDF
| 4/4/23 |
| Homework 7: PDF
| 4/13/23 |
| Homework 8: PDF
| 5/4/23 |
Course Schedule
| Date |
Lecture Content |
Reading |
Notes |
| 1/17/23 |
Vectors. Addition and scalar multiplication. Some linear combinations. |
§ 1.1 |
lec01 |
| 1/19/23 |
Lengths and angles. Dot product. |
§ 1.2 |
lec02, vector rules |
| 1/24/23 |
Lines in 2D and 3D. Planes in 3D. |
|
lec03 |
| 1/26/23 |
More on planes in 3D. Cross product. |
|
lec04 |
| 1/31/23 |
More examples. Systems of linear equations: Row/Column Pictures. |
§ 2.1 |
lec05 |
| 2/2/23 |
Introduction to matrices. |
§ 1.3, 2.1 |
lec06 |
| 2/7/23 |
Intro to Elimination. |
§ 2.2 |
lec07 |
| 2/9/23 |
The Elimination Algorithm. |
|
lec08 |
| 2/14/23 |
Matrix multiplication and other operations. |
§ 2.4 |
lec09 |
| 2/16/23 |
Inverse Matrices. Elimination, permutation, diagonal matrices. |
§ 2.5, 2.3 |
lec10 |
| 2/21/23 |
Elimination with matrices. Finding inverses. |
§ 2.3, 2.5/6 |
lec11 |
| 2/23/23 |
LU decomposition of matrices. |
§ 2.6 |
lec12 |
| 2/28/23 |
Midterm 1 Practice Problems: pdf Practice solutions: pdf |
|
exam 1 solns |
| 3/2/23 |
Vector spaces and subspaces. |
§ 3.1 |
lec13 |
| 3/7/23 |
Spans and Column spaces. |
§ 3.1 |
lec14 |
| 3/9/23 |
Null spaces. Rank-Nullity Theorem. Independence. |
§ 3.2, 3.4 |
lec15 |
| 3/14/23 |
Spring break |
|
|
| 3/16/23 |
Spring break |
|
|
| 3/21/23 |
Independence and Bases. |
§ 3.4 |
lec16 |
| 3/23/23 |
Dimension. Reprise of Rank-Nullity Theorem. |
§ 3.4, 3.5 |
lec17 |
| 3/28/23 |
Application: interpolating data using polynomials. |
|
lec18 |
| 3/30/23 |
Intersections and sums of vector spaces, and more. |
|
lec19 |
| 4/4/23 |
Orthogonality. Projections. |
§ 4.1, 4.2 |
lec20 |
| 4/6/23 |
Least squares approximation. |
§ 4.3 |
lec21 |
| 4/11/23 |
Orthonormal bases. Gram-Schmidt. |
§ 4.4 |
lec22 |
| 4/13/23 |
QR-factorization. Introduction to determinants. |
§ 4.4, 5.1 |
lec23 |
| 4/18/23 |
Midterm 2 Practice Problems: pdf Practice solutions: pdf |
|
exam 2 solns |
| 4/20/23 |
Determinants: cofactors, inverses, volume. (Pre-recorded lecture) vid1 vid2 |
§ 5.2, 5.3 |
lec24 |
| 4/25/23 |
Eigenvalues and Eigenvectors. |
§ 6.1, 6.2 |
lec25 |
| 4/27/23 |
Diagonalization of matrices. Cayley Hamilton Theorem. |
§ 6.1, 6.2 |
lec26 |
| 5/10/23 |
Final Exam (Wednesday May 10, 11am-1:30pm, usual classroom). Additional practice problems: pdf Practice solutions: pdf |
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