### Sidebar

#### Old Announcements:

The course coordinator posted three of his latest quizzes on his website. It would be a good idea to go through them.

Here are some solutions to the modified Test 1 corrections. This document tries to explain a few fundamental things. Minor correction:

• The general fact in 4(b) should say that $X$ and $Y$ are subsets of some vector space (singular, not plural).

Here are solutions to the modified Test 2 corrections: problems 1 through 4 (or 6), 7 through 12, and 13. Minor corrections:

• In 1(b), the i-th column is the coordinate function of $F(v_i)$ not of $F(v_n)$.
• In 3(b), the 1,3 entry of the matrix should be -1 (not -2) because $2 + 6x = 3(1 +2x) - 1(1)$.
• In 10, I forgot to change the 5 to a 3.

Here are solutions to quiz 19. After you have done the suggested problems at the course coordinator's website, here are more review problems. But be sure to practice on problems from the book since the test copies them directly. Of course, you can also go back to the study guide for the 12th/13th quiz.

Planned extra review/help:

• Monday from 12 to 2:50 in WH 309. (Directions below:*)
• Tuesday from 2 to 4 in WH 309

*WH 309 is in the same hallway as my office. So the review is in a different wing than the math help room.

The final exam is scheduled for Wednesday, the 18th at 10:25am in LH 001.

Please see the course coordinator's website for suggested problems on the symmetric matrix theorem. (It's his May 2nd announcement.)

Here are notes on orthogonal matrices. Minor correction on the last two pages: First, page 9 should end by saying, the same reasoning gives the dot product of $Ae_i$ and $Ae_j$ equals 0. On the last page, to get all 2 by 2 orthogonal matrices, we may need to multiply a rotation matrix by one that just flips one of the two standard basis vectors.

Here are notes on the concept of linearly independent subspaces. Note: the concept is widespread, but this terminology is not. [Added on 5/11/16: I just found out that the terminology “linearly independent subspaces” is used in a standard book by Hoffman and Kunze in the direct-sum decomposition section.]

The 19th quiz is scheduled for Monday, May 9th. It will include all material covered in the entire course, and it will be worth at least 20 to 30 points. For the latter part, expect Gram-Schmidt to be on it as well as an application of the symmetric matrix theorem (page 275).

The 18th quiz is scheduled for Friday, May 6th. Besides possible bonuses, it will only be fill-in-the blank for (1) Theorem 7.2.3 (The symmetric matrix theorem, page 275), (2) the definition of orthogonal matrix (and Lemma 6.2.14, page 261), and (3) Theorem 5.3.15 (the entire statement of it, page 230).

The seventeenth quiz is a modified test corrections. For solutions to the test, go the the course coordinator's website (linked above) and and see his April 27th announcement(s). [Note added on 12/3/16: Parts of this assignment only makes sense when viewing the actual Test 2.]

Here are some of the quizzes we had: Quiz 9, Quiz 11, and Quiz 15.

The sixteenth quiz is scheduled for Friday, April 29th. It will cover the last part of chapter 5 (pages 228 through 234) as well as the first part of chapter 6 (pages 239 through 246). Be sure to know the definitions, lemmas, corollaries, and theorems in the stated pages. (For chapter 5, see for example the notes I wrote earlier which are slightly edited now.) Several fill-in-the blank questions will be on the quiz. There are also a couple computations that are an application of the definitions/lemmas/theorems.

Here are notes for chapter 5, since we did not finish. Reminder: be familiar with how the book words the definitions and theorems.

Starting Thursday, April 14th, on Thursdays we will meet in SL 302 (Science Library) instead of EB N25. The change is so that the university can do renovations in EB N25. This change is for the rest of the semester.

The fifteenth quiz is scheduled for Monday, April 18th. Study guide for now: just prepare for the test. (Do the coordinator's quizzes etc.)

The fourteenth quiz is scheduled for Friday, April 15th. Here is a study guide. Summary: it will cover most of chapter 5 (determinants, eigenvalues, etc.)

The 12th quiz [printed as the 13th quiz] is scheduled for Monday, April 11th. Here is the study guide. A bonus question on eigenvectors/ eigenvalues may be included.

Here is the homework assignment due today (Friday). [This was graded as being a 5 point quiz (quiz 12).]

The eleventh quiz is planned for Wednesday, April 6th. It will mostly (only?) cover sections 4.6 through 4.8 from the book. For a study guide, see WebWork ch4hw1, as well as the course coordinator's quiz 7 that he posted on March 23rd.

The tenth quiz will be a take-home quiz: Here is the assignment, which is a modified “test corrections”. There are three bonus question on it. It is due the Friday before Spring break. As motivation, recall that the final is cumulative and worth 40% of your grade; also, the class itself is cumulative. [Note added on 12/3/16: Parts of this assignment only makes sense when viewing the actual Test 1.]

The ninth quiz is planned for Thursday, March 24th. You will be asked

• to define linear dependence
• two conditions equivalent to linear dependence or two conditions equivalent to linear independence
• a few questions on Null space/kernel
• to apply the rank plus nullity theorem (dimension of column space + dimension of kernel = dimension of domain)
• to write the coordinate vector of a given vector with respect to a given basis
• theorems 4.3.1/4.3.2

To study, you should finish all the chapter 3 WebWork homework and do the first problem (or so) of ch4hw1.

The eighth quiz is scheduled for Wednesday, March 16th. It will include (a) WebWork Ch3HW2, (except the last two problems), (b) some of the first five problems of Ch3hw3, and (b) the theorems stated in class the last few days (including the end of chapter 3 and the beginning of chapter 4).

You are encouraged to look at the class notes the course coordinator puts online, from his section. In particular, check out the quizzes he gave, whic can now be found directly from his main page.

Test 1 is scheduled for Monday, March 7th at 7:35pm (in room EB 110 for our section). Here is a study guide to help you focus on the right things. Of course, you should also do the practice tests and review the study guides for the previous quizzes (either linked to or posted directly) at the old announcements page.

The seventh quiz will be a short one on Monday, March 7th. To prepare, look at the study guide for Test 1, in particular the two bullet points that say “Spend extra time on…” Besides that, there is a bonus question from chapter 3.

Elijah Swift, a tutor from the University tutoring services, will hold a review session for the test on Sunday, March 6th from 3 to 5 P.M. It will be in Lecture Hall 3.

The sixth quiz will be on Friday, March 4th. One question will be like one of the practice problems below. The other questions will test knowledge of span, linear independence/dependence, and subspaces. For practice, do problems 1 through 5 in WebWork Ch3HW1. Also do exercises 1 through 4 on page 126.

Here are a few nice practice problems. One of the next quiz problems is like this.

The fifth quiz is scheduled to be only five minutes on Friday, February 26th. The only question on it is to list conditions equivalent to a square matrix being invertible.

The fourth written quiz is scheduled for Thursday, February 25th. Here is a study guide. It will be on inverses, elementary matrices, and finding matrices that represent linear transformations. You should do Ch2HW3 and Ch2HW4 for practice (as well as Ch2HW2).

The third written quiz is scheduled for Friday, February 19th. Here is a study guide.

The second written quiz is scheduled for Thursday, February 11th. You should know the following:

• The book's definition of a linear transformation
• The ability to determine if a given function is a linear transformation (Be sure to check out the exercises in the book on page 46.)
• one-to-one functions defined by matrices (See WebWork homework 3 and theorem 1.6.8 on page 34.)
• onto functions defined by matrices (Also read Corollary 1.6.9.)
• For the bonus question: matrix multiplication

The first written quiz is scheduled for Wednesday, February 3rd. You should know the following:

• linear combinations
• elementary row operations
• row equivalence of matrices
• reduced row echelon form
• shape of a matrix
• pivot columns
• rank of a matrix
• solving a system of linear equations
• the definitions and lemma on page 29 (homogeneous system of linear equations)

Not every old announcement is written here, and part of at least one announcement has been deleted.