# MAT 331 Calendar Spring 2014

This is a tentative calendar. I may have to move some things as we go along but I'll try to avoid moving the test days so you can plan ahead.

Chapters and sections refer to our textbook, Linear Algebra by Cherney, Denton, and Waldron.

Most of the homework assignments are on WeBWorK http://math.csudh.edu/webwork2/14Spring_MAT331_Jennings

• 1st week, Jan. 20, 22
• Mon. Jan. 22 Rev. Martin Luther King Holiday
• Ch 1. What is Linear Algebra?
• 2nd week, Jan. 27, 29
• Sec. 2.1 Gaussian Elimination
• Sec. 2.2.1-2 Elementary Row Operations
• Homework: Write up section 2.2 Review Problems #1, 3, 4, 5, 9. Due Wednesday, Feb. 5
• Two examples of solving equations with Gauss-Jordan elimination using a computer, including the example from Wednesday's lecture.
• For a little history, see Wikipedia articles on Carl Friedrich Gauss and Wilhelm Jordan.
• 3rd week, Feb. 3, 5
• Sec. 2.2.3-4 Row Op's, LU, LDU, LDPU Factorizations
• (Skip Ch. 3 The Simplex Method -- we'll do that later if we have time.)
• 4th week, Feb. 10, 12
• Elementary matrices, matrix multiplication
• 5th week, Feb. 17, 19
• Mon. Feb 17 Presidents' Day Holiday
• First Midterm Exam Wednesday, Feb. 19 Solutions
• Ch. 4 Vectors in Space, n-vectors. (Most of this is a review of Calculus III).
• Paper-and-pencil homework: 4.5 Review problems #1,2. Due Monday Mar. 3. (Changed from Feb. 26.)
• 6th week, Feb. 24, 26
• Continue with chapter 4. Finish last week's homework. Start reading chapters 5 and 6 so you'll be prepared for next week.
• 7th week, Mar. 3, 5
• Ch. 5 Vector Spaces. Paper-and-pencil homework: Review problems #3, 5a,b, 9. Due Monday Mar. 10. There are typos in problems 3 and 9. In problem 3 both limits should be $$\lim_{n\to\infty} f(n)$$ (they left out "$$(n)$$"). In problem 9 the set $$S$$ should be nonempty and the "mapping" should go from $$S$$ to $$V$$ not the other way around. Here is a rewording of problem 9:
Problem 9 (corrected). Let $$V$$ be a vector space and let $$S$$ be any nonempty set. Let $$V^S$$ be the set of all functions $$f\colon S \to V$$ that map $$S$$ to $$V$$. Show that $$V^S$$ is a vector space.
(Hints for problem 9. A function $$f\colon S \to V$$ is a function whose domain is $$S$$ and whose range is $$V$$. These functions are the "vectors" in the set $$V^S$$. First decide what "addition" and "scalar multiplication" of these "vectors" mean: if $$f,g\colon S\to V$$ are functions that map $$S$$ to $$V$$ then how is the function $$f+g$$ defined? If $$r\in \mathbb{R}$$ is a scalar then how is the function $$r f$$ defined? What function plays the role of zero? Then, when you have defined addition and scalar multiplication and zero, check that all the properties of a vector space are true for the set of functions in $$V^S$$.)
• Handout: proof that the set of real valued functions on a finite set is a vector space.
• Ch. 6. Linear Transformations. Paper-and-pencil homework: Review problems #2, 4, 5. In #2 assume $$f\colon\mathbb{R}\to\mathbb{R}$$. Due Wednesday Mar. 12
• 8th week, Mar. 10, 12
• Live demo bases of $$\mathbb{R}^2$$.
• Sec. 7.1 Linear Transformations and Matrices
• 9th week, Mar. 17, 19
• Sec. 7.2-3 Properties of Matrices, Inverse Matrices
• 10th week, Mar. 24, 26
• Mar. 31. Apr. 4 Spring Recess
• 11th week, Apr. 7, 9
• 12th week, Apr. 14, 16
• Ch. 9 Subspaces and Spanning Sets
• Ch. 10 Linear Dependence
• 13th week, Apr. 21, 23
• Ch. 11 Basis and Dimension
• 14th week, Apr. 28, 30
• 15th week, May 5, 7
• Final exams week