Math 310

Instructor: John Lesieutre
Meetings: MWF 1:00-1:50 (Lecture Center D5)
Email: jdl@uic.edu
Office hours: Tu 3-4,Th 3-4, F 10-11 (in SEO 411)

The textbook for the course is Linear Algebra and Its Applications (5th edition) by Lay, Lay, McDonald.

Syllabus and course info

The final exam will take place Monday, 12/7 from 1-3 in Lecture Center D5 (the usual class room). Please don't miss it!

Final review sheet
Complete scanned notes
Practice final, Solutions

Review sheet 2
Practice test 2, Solutions

Review sheet 1
Practice test 1, Solutions

Links:
Blackboard (grades)
Piazza (discussion)
General math 310 info This site has useful things like a glossary and old exams, but includes exam dates for a different section! Ignore these!



Schedule and notes
8/24 1.1: Linear systems lecture HW: 1.1.2, 1.1.13, 1.1.17 (problems, solutions)
8/26 1.2: Row reduction and echelon forms lecture HW: 1.2.2, 1.2.3, 1.2.4 (problems, solutions)
8/28 1.3: Vector equations lecture HW: 1.2.7, 1.2.12, 1.3.1, 1.3.3, 1.3.9 (problems, solutions)
8/31 1.4: The matrix equation Ax=b lecture HW: 1.3.11, 1.3.18, 1.4.1, 1.4.3, 1.4.10 (problems, solutions)
9/2 1.5: Solution sets of linear systems lecture, quiz HW: 1.5.5, 1.5.7, 1.5.9, 1.5.15, 1.5.17 (problems, solutions)
9/4 1.6: Applications of linear systems lecture HW: 1.6.1, 1.6.5, 1.6.6, 1.6.11 (problems, solutions)
9/9 1.7: Linear independence lecture, quiz HW: 1.7.1, 1.7.4, 1.7.9, 1.7.29, (problems, solutions)
9/11 1.8: Linear transformations lecture HW: 1.8.1, 1.8.3, 1.8.15, 1.8.16 (problems, solutions)
9/14 1.9: Matrix of a linear transformation lecture HW: 1.9.2, 1.9.4, 1.9.13, 1.9.19 (problems, solutions)
9/16 1.10: Linear models in business, science, and engineering lecture, quiz HW: 1.9.26, 1.10.5, 1.10.9 (problems, solutions)
9/18 2.1: Matrix operations lecture HW: 2.1.1, 2.1.3, 2.1.5, 2.1.10 (problems, solutions)
9/21 2.2: Inverse of a matrix lecture HW: 2.2.1, 2.2.5, 2.2.31, transformation problem (see pdf) (problems, solutions)
9/23 2.3: Characterization of invertible matrices lecture, quiz HW: 2.3.1, 2.3.3, 2.3.13, 2.3.15 (problems, solutions)
9/25 Leftovers, 2.5: Matrix factorizations lecture HW: 1.10.9, 2.5.1, 2.5.9 (problems, solutions)
9/28 3.1: Introduction to determinants lecture HW: 3.1.1, 3.1.4, 3.1.9, 3.4.15, 3.4.19 (problems, solutions)
9/30 Midterm 1 exam, solutions
10/2 3.2: Properties of determinants lecture HW: 3.2.5, 3.2.11, 3.2.24, 3.2.29 (problems, solutions)
10/5 3.3: Cramer's rule, volume and linear transformations lecture HW: 3.3.1, 3.3.7, 3.3.11, 3.3.20, 3.3.29 (problems, solutions)
10/7 4.1: Vector spaces and subspaces lecture, quiz HW: 4.1.1, 4.1.3, 4.1.5, 4.1.7 (problems, solutions)
10/9 4.2: Null spaces, column spaces, and linear transformations lecture HW: 4.1.11, 4.2.4, 4.2.7, 4.2.15, 4.2.17 (problems, solutions)
10/12 4.3: Linearly independent sets; bases lecture HW: 4.3.3, 4.3.9, 4.3.15, 4.3.34 (problems, solutions)
10/14 4.4: Coordinate system lecture, quiz HW: 4.4.3, 4.4.5, 4.4.7, 4.4.12, 4.4.14 (problems, solutions)
10/16 4.5: The dimension of a vector space lecture HW: 4.5.1, 4.5.5, 4.5.11, 4.5.21 (problems, solutions)
10/19 4.6: Rank lecture HW: 4.6.1, 4.6.2, 4.6.8, 4.6.9, 4.6.22 (problems, solutions)
10/21 4.7: Change of basis lecture, quiz HW: 4.7,1, 4.7.7, 4.7.9, 4.7.13 (problems, solutions)
10/23 4.9: Applications to Markov chains lecture HW: 4.9.1, 4.9.4, 4.9.7, 4.9.11 (problems, solutions)
10/26 5.1: Eigenvectors and eigenvalues lecture HW: 5.1.1, 5.1.2, 5.1.15, 5.1.18, 5.1.19 (problems, solutions)
10/28 5.2: The characteristic equation lecture, quiz HW: 5.2.1, 5.2.5, 5.2.9, 5.2.12, 5.2.15 (problems, solutions)
10/30 5.3: Diagonalization lecture HW: 5.3.1, 5.3.3, 5.3.7, 5.3.11 (problems, solutions)
11/2 5.4: Eigenvectors and linear transformations lecture HW: 5.4.11, 5.4.13, Fibonacci problem in pdf (problems, solutions)
11/4 Eigenvector review, Appendix B: complex numbers lecture, quiz HW: 5.4.18, complex numbers problems in pdf (problems, solutions)
11/6 5.5: Complex eigenvalues lecture HW: 5.5.1, 5.5.4, 5.5.9, 5.5.13 (problems, solutions)
11/9 5.7: Applications to differential equations lecture HW: 5.7.1, 5.7.7, 5.7.9 (problems, solutions)
11/11 Midterm 2 exam, solutions
11/13 6.1: Inner product, length and orthogonality lecture HW: 6.1.1, 6.1.14, 6.1.16, 6.1.26 (problems, solutions)
11/16 6.2: Orthogonal sets lecture HW: 6.2.1, 6.2.8, 6.2.10, 6.2.12, 6.2.13 (problems, solutions)
11/18 6.3: Orthogonal projections lecture, quiz HW: 6.3.3, 6.3.9, 6.3.12, 6.3.15 (problems, solutions)
11/20 6.4: The Gram--Schmidt process lecture HW: 6.4.1, 6.4.9, 6.4.10, 6.4.13 (problems, solutions)
11/23 6.5: Least-squares problems lecture HW: 6.5.9, 6.5.12, 6.6.2, 6.6.3 (problems, solutions)
11/25 6.6: Application to linear models lecture, quiz HW: 6.5.3, 6.5.15, 6.6.8, 6.6.9 (problems, solutions)
11/30 7.1: Diagonalization of symmetric matrices lecture HW: none, but could be on final
12/2 7.4: The singular value decomposition lecture, quiz
12/4 Review lecture Good luck!



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