**Class Schedule**

All textbook sections come from the course textbook. Your homework sets also use many problems from that textbook.

- The problem text may be recopied in homework assignments, so that you can do problems without having to keep your book open all the time.
- For more details, consult the syllabus found in the sidebar to this page.

Many handouts are attached in this calendar, such as classwork solutions and HW assignments.

- Partial solution sets can instead be found on eLC.

Expect this calendar to be updated about once a week. Definitely check back on Mondays and Fridays.

**UNIT 1: Vector geometry, matrix systems, judging existence and uniqueness of solutions**

*Week 1:*

*W Jan 9:*Introduction to course, Section 1.1. Basic pictures of vectors, drawing the vectors x + y and x - y.*F Jan 11:*Section 1.1. Span of vectors, parametric equations for lines and planes.

**HW 1, due F Jan 18 at the start of class**

- For those who don't have the book yet, here are scans of Section 1.1 HW and Section 1.2 HW.
- Most assignments will be due on Mondays, but this first assignment will be due on a Friday because of the holiday on Monday January 21.
- Partial solutions to HW assignments get uploaded to the Content area of eLC one class day after the HW is due (to account for anyone who turns in the HW late).

Extra handout of the week: Multiple ways to write the same line or the same span

- We'll have supplemental material posted on most weeks to provide extra practice and go through some proofs slowly.

*Week 2:*

*M Jan 14*. Start Section 1.2: Dot product, orthogonal vectors, angle between vectors.*W Jan 16*. Finish 1.2: Projections onto vectors, Cauchy-Schwarz Inequality.*F Jan 18*. 1.3: The normal equation a*x = c, hyperplanes.

HW 1 was assigned last week... check it out! It's due this Friday in class.

Extra handout of the week: Cauchy-Schwarz revisited, and lots of demonstration of intersections

*Week 3*:

*No class on M Jan 21*.*W Jan 23*. Start 1.4: Row operations to simplify linear equations, matrix notation, echelon form.- In-class exercises (demonstrated in class instead of group-work)

*F Jan 25*. Finish 1.4: More matrix practice, rank of a matrix, reduced echelon form.- In-class exercises (demonstrated in class instead of group-work)

HW 2's link can be found in last week's calendar area. It's due M Jan 28.

Extra handout of the week: Some more practice with linear systems and echelon form

*Week 4:*

*M Jan 28*. Start 1.5: Linearity of Ax and column space, constraint equations for consistency.*W Jan 30*. Finish 1.5: Unique or infinite solutions to Ax = b, non-singular square matrices.*F Feb 1*. Start 1.6: Several applications of systems Ax = b, such as mixing quantities, balancing chemical reactions, and fitting a polynomial curve through several points.

- This assignment has a few small proofs on it. Make sure you start this by Wednesday to have enough time to bring up questions outside of class!

Extra handout of the week: Existence of matrices with certain properties, and an application to partial fractions

*Week 5:*

*M Feb 4*. Finish 1.6 and start 2.1: Probability matrices (discrete systems), definition of A + B and AB.*W Feb 6*. Finish 2.1, start 2.2: Important properties and examples of product AB, powers A^k of square matrices, linear transformation definition.*F Feb 8*. Finish 2.2: The standard matrix of a linear transformation, useful geometric examples like projection and rotation.

- The handout for the week can provide another useful example of a probability matrix (to help with #2).

Extra handout of the week: A probability matrix problem, exploring when AB = BA, and a neat rotation fact

*TEST 1 IS NEXT FRIDAY, FEBRUARY 15.*

- You get 55 minutes, as opposed to 50. If this is not possible with your class schedule, let me know so we can work out alternate arrangements.
- Expect 5 or 6 questions covering Sections 1.1 to 2.2, HWs 1 through 4.
- The material from M Feb 11 will not be on this exam.

- Non-graphing calculators are allowed as long as they can't do matrix algebra for you. (See the syllabus.)
- A topic list (with a theorem summary) for Test 1
- Practice questions for Test 1 (now with solutions for several problems)
- We will have an in-class review day on W Feb 13.

*Week 6:*

*M Feb 11*. 2.3: Inverse matrices with AB = BA = I.*W Feb 13*. In-class review for Test 1 (see practice questions!)*F Feb 15*.**TEST 1 (55 minutes)**

There's no HW for this week.

There's no extra handout for this week. Look at test review links from the end of last week!

**UNIT 2: More abstract properties about matrices, vector subspaces, and linear transformations**

*Week 7:*

*M Feb 18*. Finish 2.3, Start 2.4: Facts about inverses, elementary matrices, and constructing an LU-decomposition.*W Feb 20*. Finish 2.4, complete 2.5: Using LU-decomposition to solve equations, transposes of matrices.*F Feb 22*. Start 3.1: subspaces of R^n, with some key examples involving span and nullspace, intersection of two subspaces.

Extra handout of the week: LU-decomposition practice, and some discussion on using transposes for rows

*Week 8:*

*M Feb 25*. Finish 3.1, Start 3.2: Orthogonal complements ("perp spaces"), nullspace and rowspace.- In-class practice (with some short proofs)

*W Feb 27*. Finish 3.2: column space and left nullspace.*F Mar 1*. Start 3.3: linearly independent sets of vectors.

- There will be a very short HW 7 released that Monday, due on that Friday (just before break).

Extra handout of the week: Calculating some orthogonal complements, verifying V = (V^perp)^perp

*Week 9:*

*M Mar 4*. 3.3: Basis of a vector space, several examples of bases with our four subspaces.*W Mar 6*. Start 3.4: Dimension dim(V), the four subspace bases.- The handout for this week (see below) explores this more thoroughly with LU-decompositions.

*F Mar 8*. Finish 3.4: Dimension of V^{perp}, V + V^{perp} = R^n.

- You should be able to handle the first four problems after Monday's class. There are 7 problems total.
- I'll hold extra office hours this week on Tuesday 3:00-4:30 for help with this.

Extra handout of the week: A linear independence proof example, LU-decomposition with our four subspaces

*Hope you have a good Spring Break!*

*Week 10:*

*M Mar 18*. Brief coverage of 3.6: Abstract vector space properties (examples featuring functions, matrices, and polynomials), inner products (generalization of dot product), LaGrange's polynomial interpolation.*W Mar 20*. Start 4.1: Projection onto arbitrary subspaces V, least-squares approximation of Ax = b by solving A^T A x = A^T b.- In-class demonstration
- Also check out the weekly handout below to see more discussion of projection matrices P_V!

*F Mar 22*. Finish 4.1, Start 4.2: Lines of best fit, orthogonal and orthonormal sets, Gram-Schmidt process to make orthogonal sets.

Extra handout of the week: More practice with projection, and properties of P_V

*Week 11:*

*M Mar 25*. Finish 4.2: Projection examples with orthogonal bases, unique preimages in R(A) (see end of Section 3.4 too)*W Mar 27*. Start 4.3: Transformation matrices, change of basis formulas*F Mar 29*. Finish 4.3: More practice with change of basis (especially projections and reflections), similar matrices.

Extra handout of the week: Practice with change of base, similarity

*TEST 2 IS NEXT FRIDAY, APRIL 5.*

- You get 55 minutes, as opposed to 50. I can start the test early for some of you if you cannot stay after class for 5 extra minutes.
- Expect 5 questions covering Sections 2.3 to 4.3, HWs 5 through 9.
- The material from M Mar 1 will not be on this exam.
- Section 3.6 will not be on this exam (abstract vector spaces).
- Similar matrices (end of 4.3) will not be on this exam.

- Non-graphing calculators are allowed as long as they can't do matrix algebra for you. (See the syllabus.)
- Topic list for review
- Practice questions for the exam
- We will have an in-class review day on W Apr 3.
**Bring HW question suggestions you would like to go over on review day!**

*Week 12:*

*M Apr 1*. Start 5.1: Introduction to the determinant of a square matrix, det(A).- This material is not covered on Test 2.

*W Apr 3*. In-class review for Test 2.*F Apr 5*.**TEST 2**

There's no HW this week.

There's no extra handout from this week. Look up test review materials!

**FINAL UNIT: Determinants and eigenvectors**

*Week 13:*

*M Apr 8*. 5.1: The fundamental properties of determinants det(A).*W Apr 10*. 5.2: Cofactor expansion, Cramer's Rule.*F Apr 12*. 5.3: Using the determinant for area and volume, cross product in 3D.

Extra handout of the week: Cofactor practice (especially with det(A - tI)), and remarks about permutations

*Week 14:*

*M Apr 15*. 6.1: Definitions of eigenvalues and eigenvectors for square matrices A.*W Apr 17*. 6.1, 6.2: More practice with eigenvalues and eigenvectors, some basic properties related to similar matrices or transposes, algebraic versus geometric multiplicity*F Apr 19*. 6.2, start 6.3: More properties of eigenvalues and eigenvectors, using the diagonalized representation to compute matrix powers A^k- In-class demonstration
- We resume with this topic next Monday. You may want to read ahead in the text up until subsection 3.1 in Section 6.3. (We won't go into that subsection.)

- This is the last HW set for the course.
- It is NOT due on a Monday! It is due on a Wednesday. Use this opportunity to attend office hours on Monday or Tuesday of the next week? (I'll post some Tuesday hours next week.)

Extra handout of the week: Eigenvector computation, powers of a diagonalizable matrix from HW 4!

*Week 15 and last day of class:*

*M Apr 22*. Finish 6.3: applications of matrix powers A^k to probability systems (stochastic matrices) and to linear recurrences.*W Apr 24*. Parts of 6.4: complex numbers as eigenvalues, the Spectral Theorem.**This material is not tested on the final exam.**

*F Apr 26 and M Apr 29*. Final Exam Review- Maybe we go over the old exam ideas in class?
- Topic list for determinants and eigenvectors
- There may or may not be practice questions for this material though.
- I am not creating a course-long topic list for the entire semester.

- Please bring questions (especially more open-ended topic questions) to go over.
**If you email me ahead of time, I'll do my best to accommodate your request**.

**FINAL EXAM INFORMATION**

**Exam date and time:**Monday May 6, 12pm to 3pm, in our usual classroom (Dance 304)- Expect the exam to be around 10 or 11 questions, for a three-hour test.
- I would expect 3 or 4 questions based on each of the two previous tests, as well as 1 or 2 problems involving determinants and eigenvalues.
- Expect one question at the beginning which tests your knowledge of crucial definitions or theorem statements from this course!

**Final exam policies:**- Leave all bookbags at the side of the room once the test starts.
- Any phones or Internet-enabled devices should be turned off and left in bookbags.
- Only one student may go to the bathroom at a time, barring any emergency circumstances.

Last updated: 4/23/2019