MTH 210-E: Introduction to Linear Algebra

University of Miami, Spring 2022

Instructor: Christopher Scaduto
Email: c.scaduto @ math.miami.edu
Office: Ungar 525
Office hours: W 10:30-12:00 (or by appointment)
Each office hour session is currently on Zoom.

Class Time and Location: MWF 1:00-1:50 in Dooly Memorial 100.
Note that class meets on Zoom until in-class lectures begin on January 31, 2022.

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.

Homework Assignments


Assignment Due Date
Homework 1: PDF 1/31/22
Homework 2: PDF 2/11/22
Homework 3: PDF 2/23/22
Homework 4: PDF 3/7/22
Homework 5: PDF 3/11/22
Homework 6: PDF 3/30/22
Homework 7: PDF 4/8/22
Homework 8: PDF 4/25/22
Homework 9: PDF 5/4/22


Course Schedule

Date Lecture Content Reading Notes
1/19/22 Introduction to the course. Syllabus. Vectors and linear combinations. § 1.1 lec01
1/21/22 Lengths and angles. Dot product. § 1.2 lec02, vector operation rules
1/24/22 More dot product. Lines in R^2. § 1.2 lec03
1/26/22 Lines in R^2 and planes in R^3. lec04
1/28/22 Planes and hyperplanes. Cross product. lec05
1/31/22 Intersecting lines. Vector equations. § 2.1 lec06
2/2/22 Row/column pictures. Two planes in R^3. First look at matrices. § 2.1 lec07
2/4/22 Matrices and linear equations. § 1.3, 2.1 lec08
2/7/22 Idea of Elimination § 2.2 lec09
2/9/22 Towards elimination with matrices § 2.3 lec10
2/11/22 Elimination algorithm. RREF. lec11
2/14/22 More elimination! Elimination matrices § 2.3 lec12
2/16/22 Matrix multiplication and other operations. § 2.4 lec13
2/18/22 Back to Elimination...using matrices. § 2.3, 2.6 lec14
2/21/22 Inverses of matrices. § 2.5 lec15
2/23/22 Computing inverses of matrices. § 2.5 lec16
2/25/22 LU decomposition. § 2.6 lec17
2/28/22 Some practice problems lec18 (solutions)
3/2/22 Midterm 1 solutions
3/4/22 Vector spaces and subspaces. § 3.1 lec19
3/7/22 More subspaces. Spans and column spaces. § 3.1 lec20
3/9/22 Examples of column spaces. § 3.1 lec21
3/11/22 Nullspaces. Statement of Rank-Nullity Theorem. § 3.2, 3.5 lec22
3/14/22 Spring recess
3/16/22 Spring recess
3/18/22 Spring recess
3/21/22 Linear independence. § 3.4 lec23
3/23/22 Bases of vector spaces. § 3.4 lec24
3/25/22 Dimension. § 3.4 lec25
3/28/22 Rank-Nullity Theorem (reprise) § 3.5 lec26
3/30/22 Application: interpolation & polynomials lec27
4/1/22 Intersections of subspaces lec28
4/4/22 Orthogonality. Intro to projections. § 4.1, 4.2 lec29
4/6/22 Projections continued. § 4.2 lec30
4/8/22 Review Some practice problems solns, scraps
4/11/22 Midterm 2 solutions
4/13/22 Least squares approximations § 4.3 lec31
4/15/22 Gram-Schmidt orthogonalization § 4.4 lec32
4/18/22 Gram-Schmidt (cont). QR factorization. Determinants. (pre-recorded) § 4.4, 5.1 lec33
4/20/22 Determinants, continued. (pre-recorded) § 5.2 lec34
4/22/22 Determinants: cofactors, inverses, volume. (pre-recorded) § 5.3 lec35
4/25/22 Intro to eigenvalues and eigenvectors. § 6.1, 6.2 lec36
4/27/22 Eigenvalues and eigenvectors, continued. § 6.1, 6.2 lec37
4/29/22 Jordan Normal Form and Cayley-Hamilton Theorem. lec38
5/2/22 Review Some practice problems solutions
5/4/22 Final Exam 2:00PM-4:30PM