# MA322-001

Wed Jan 15: First day of class. Went over the syllabus. Worked out part of example 1 in the textbook. You are responsible for reading all of 1.1 and solving #5,#9,#17+18(just explain how to do it), 23, 29, 31, 33, 34. I handed out the quiz but we didn't have time to do it. You can check your work against the answer key.

Thu: Make sure to reread 1.1, work on the homework, and skim 1.2.

Fri Jan 17: Second day of class. We worked a full example, and carefully described what the solutions look like, and how we managed to solve it. The quiz covered HW 1.1 and what we did in class. You can check your answers; most people did extremely well, and everybody did well enough. Bold words we covered were: free variables, pivots, echelon form, reduced echelon form. We technically just learned Gaussian elimination as well. Before class started, we played and analyzed a silly game:

Game: Here is a silly game based on magic squares (add up the rows and get the same number for each row, add up the columns and get the same number of each column; we play on easy difficulty: the row sum is not required to be the same as the column sum). The first player gets two moves in a row; then the second player has to finish the magic square, if they can! Can they? Who has the advantage?

Sat-Mon: Reread 1.2, work on the homework, and skim 1.3. Here is a worked version of HW 1.2 #7. You may also find page 51 useful, as we'll use that idea (stoichiometry) for our example.

Wed Jan 22: Third day of class: 1.3 and stoichiometry. We covered vector geometry (walking on the lattice, example 4) and some stoichiometry (section 1.6 page 51). We took notes on a worksheet (the quiz is on the last page). You can check your work here. The “harder stoichiometry” problem is for you to try if like to test whether you've figured it out. Quiz question #3 was too soon, we'll handle it Friday (also it had a typo! Fixed on the online version, and here is the updated key).

HW 1.3 changed to HW 1.3 #5, 7, 9, 11, 13*, 22, 29*. For 13, convince yourself it is solved the same way as 11. Read 29, and convince yourself that it makes sense. You don't need to do the calculations on these two if you are pressed for time.

Fri Jan 24: Fourth day of class: 1.4 and stoichiometry. We went over the answers to Wednesday's quiz carefully, including a stoichiometry worksheet. We discussed how vectors are just lists of numbers, and answers are just lists of numbers, so answers are vectors. In our stoichiometry example, we wrote the answer as a line in vector form, and then covered how to find the (vector) equation of a line between two points. Importantly, slope is now a vector rather than a ratio. This is also called parametric form. We didn't have time for the quiz, but I'll collect it at the beginning of class on Monday.

Extra homework: Finish the quiz from Friday.

Mon Jan 27:Fifth day of class: 1.4 and 1.5. We'll finish up 1.4 and 1.5, making sure to cover all the different ways of writing down both the questions and the answers. Particular and homogeneous solutions. Vector form of the solution. The quiz from Friday is due at the beginning of class. You can check your answer here. We also had a quiz today; answers will be posted soon.

Tue Jan 28:9:30am to 10:30am special MA322 office hours.

Wed Jan 29:Sixth day of class: (1) Equation of a plane, (2) when can we find a particular solution, (3) Review all the ways to ask the same question (systems of equations, vector equation=span=linear combination, matrix equation), all the ways to write down the answer (basic and free variables, particular and homogeneous, vector form). Review the only way we know to solve them (guassian elimination). Review stoichiometry if time.

Fri Jan 31: Seventh day of class: EXAM. People did pretty well. If you made B- or less, make sure to seriously restudy this material. These sorts of questions will keep coming up in this class. If you made an A or less it doesn't hurt to review the parts you missed, but much of it should be come clear as we keep working. Solution key available end of today.

Mon Feb 3: Class cancelled by UK. It was going to be awesome too. With sledding. Since I couldn't return your exams, I put the grade on blackboard.

Wed Feb 5: Exams 1.7 Linear dependence AND exam return. You can check your work on the take home quiz. HW1.7 #1,9,15*,17*,19* (the star means no calculations needed).

Fri Feb 7: 1.8 linear transformations and 1.9 their matrices. These two topics go together wonderfully. You can check your work on the quiz . HW1.8 #1,13,14,15,16,19. HW1.9 #1*,3*,5*,13*,15*

Mon Feb 10: 2.1 Matrix operations (adding matrices, multiplying by a scalar, transpose, matrix multiplication). You can check you work on the quiz. HW2.1 #1,5,7*,10,11,12

Wed Feb 12: 2.2 Matrix inversion (when does a matrix have an inverse, how to find it, elementary matrices). The quiz is take-home, but you can check your work on this partial solution (full solution). HW2.2 #1,5,7,33

Fri Feb 14: 2.3 Matrix invertibility (when does a matrix have an inverse) The quiz was take home, and you can check your work. HW2.3 #1*,3*,5*,7*,13*

Mon Feb 17: 3.2/3.3 Matrix determinants (relationship to volume, how to actually compute them) The quiz was take home, and check your work. HW3.3#19,21,23

Wed Feb 19: Review.

Fri Feb 21: Exam

Mon Feb 24: 4.1 vector spaces: know the (10) axioms of a vector space, and the (3 part) test for a subspace. Be able to give examples of vector spaces and subspaces. HW 4.1 #1,2,3,5,6,7,8,9,11,19,21,(32,33,37). None involve computation. The last three will be used in this course, but won't be on the quiz.

Wed Feb 26: 4.2 Null spaces, column spaces, and linear transformations: Know the definition of null space, and how it relates to page 2 of exam 1 and column dependence. Know the definition of column space and how it relates to row dependence. Know the definition of linear transformation and how to use section 1.8/1.9 to think of them as matrices. The quiz is TAKE-HOME (write up solutions to the first two in your own words. I'll put up solutions as well). HW 4.1 #1,2,3,4,5,6,7,8,9,11,15,19,21 (again) and HW 4.2 #1,3,7,9,11,13,17*.

Fri Feb 28: 4.1 / 4.2 Vector spaces, subspaces, null spaces, column spaces (images). We'll go over more examples and make sure we get this. This is a very hard section, because it is all about perspective. This is the part that will actually let you use MA322 to get your job done, not just your MA322 homework. The quiz for Friday is take-home.

Mon Mar 3: Snow Day.

Wed Mar 5: 4.3. Writing down subspaces nicely. We talked about how subspaces are spans (this is like Col(A)). In 4.3, we talk about how to make sure none of the spanning vectors are redundant (this is like Nul(A)). The quiz will cover HW 4.2 #1,3,7,9,11,13,17 and the new stuff. Friday's quiz is due at the beginning of class.

Fri Mar 7: 4.4 and 4.5. Coordinate systems and dimension, especially for column spaces. The quiz.

Mon Mar 10: Review with answers.

Make sure you can answer questions like:
• Is this a subspace? Explain why or why not.
• What is the dimension of this subspace. Give a basis.
• Is this vector in this subspace? Give its coordinates with respect to this basis.
You'll need to be able to handle “subspaces” expressed as images of functions, and as solutions to equations (function value equals blah). The functions will either have domain and range column vectors (and then functions are just called matrices, like “A”), or domain and range contained in the set of real-valued functions with domain the real numbers, (and then the functions are called linear transformations, like the derivative, the definite integral, the evaluation at a point).

Wed Mar 12: Exam on 4.1 through 4.5.

Fri Mar 14: Work on the project due Fri Mar 28, 2014

Mon Mar 24: 5.1: Eigenvectors and eigenvalues. Some matrices would be diagonal if they were only given the chance to change coordinates. quiz with answers. HW5.1 #1,3,9,13,17,33 (and try #33 with A=[0,1;1,1]).

Wed Mar 26: 5.2: One way to find eigenvalues. Probably some review of diagonal matrices so that we realize how nice they are. quiz with with answers.

Fri Mar 28: Quickly go over project (Ch 4). Work on the Fibonacci fun (Ch 5). quiz it up with with answers.

Mon Mar 31: Review. I'll cover this population model (which is a very primitive version of section 5.6).

Wed Apr 2: Exam over chapter 5, with answers.

Fri Apr 4: No class. NCUR conference is using our classroom.

Mon Apr 7: 6.1 and 6.2: Inner products and orthogonality. quiz with answers.

Wed Apr 9: 6.3: Projections. quiz with answers.

Fri Apr 11: 6.4 and 6.5: Gram-Schmidt and least squares solutions. quiz with answers.

Mon Apr 14: Ch 6 review with answers.

Wed Apr 16: Ch6 exam with answers.

Fri Apr 18: Chapter 7.1: Emphasizing the so-called “spectral decomposition” of a symmetric matrix as a sum of rank one matrices uuT where the u are orthogonal column vectors. Such a sum has (uTu,u) as its eigenpairs. The quiz for today with answers. HOMEWORK: Find the spectral decomposition of the diagonal matrix with entries 1,3,5.

Mon Apr 21: Chapter 7.2: Quadratic forms, emphasizing so-called “principal axes”. Quadratic forms are basically “energy” and the principal axes allow us to find the principal contributors to both maximum and minimum energy. We'll talk about how this can be used to understand statistical energy, also known as “variance.” The worksheet and quiz with answers.

Wed Apr 23: Chapter 7.3: Constrained optimization. Actually find those minimum and maximum energies. quiz with answers.

Fri Apr 25: Chapter 7.4: SVD. We will write ANY matrix (even rectangular ones) as a sum of rank one matrices uvT where the u are orthogonal column vectors of a certain length, and the v are orthogonal column vectors of a certain (possibly different) length. Principal axes, energy levels, etc. will still basically work even for rectangular matrices. We worked the quiz together. The HOMEWORK is described on a webpage. You'll need a matrix calculator, but the homework includes a link to a free online interface to the free matrix calculator mentioned in class.

Mon Apr 28: Chapter 7.5: Image processing and statistical analysis. We reduce the dimension of statistical observations to something more managable. quiz.

Wed Apr 30: Chapter 7 review. Symmetric and rectangular; eigen and singular.

Fri May 2: Chapter 7 review. Practice exam with brief answers.