## Colorado State University, Pueblo; Fall 2011 Math 207 — Matrix and Vector Algebra with Applications Homework Assignments & Course Schedule

Here is a link back to the course syllabus/policy page.

In the following all sections and page numbers refer to the required course textbook, Linear Algebra, A Modern Introduction (2nd ed.), by David Poole.

This schedule is subject to change, but should be accurate at any moment for at least a week into the future. Please check regularly to keep an eye out for changes.

Writing Emphasis problem(s) are indicated below as "17WE", for example.

• M:
• Read: To the Student, p. xxiii and §1.1
• Content:
• bureaucracy and introductions
• what are vectors
• "=" for vectors
• components
• row- and column-vectors
• HW0: Send me e-mail (at jonathan.poritz@gmail.com) telling me:
2. Your e-mail address. (Please give me one that you actually check fairly frequently, since I may use it to contact you during the term.)
3. Your year/program/major at CSUP.
4. The reason you are taking this course.
5. What you intend to do after CSUP, in so far as you have an idea.
6. Past math classes you've had.
7. Other math and science classes you are taking this term, and others you intend to take in coming terms.
8. Your favorite mathematical subject.
9. Your favorite mathematical result/theorem/technique/example/problem.
10. Anything else you think I should know (disabilities, employment or other things that take a lot of time, etc.)
11. [Optional:] The best book you have read recently.
I will only enter your name into my gradebook when I get this e-mail, so you really need to do this assignment ASAP. Please take a moment to be complete (indeed, be as expansive as you can) — the more information I have about you, the better I can adapt the course to your needs and interests.
• W:
• Read: §§1.1 & 1.2
• Content:
• scalar multiplication
• properties of these vector operations
• the norm of a vector
• the dot product of two vectors
• R2, R3, and Rn
• a linear combination of two vectors
• unit vectors
• F:
• Today [Friday] is the last day to add classes.
• Content:
• the geometric interpretation of the dot product
• properties of dot products and norms
• projections
• the Cauchy-Schwarz-Buniakovsky Inequality
• the Pythagorean Theorem
• orthogonal vectors
• the Triangle Inequality

• M:
• Read: Exploration: Vectors and Geometry, p. 29 and §1.3
• Hand in MI1 and exercises HW1:
• §1.1: 6, 8, 10, 14, 18
• §1.2: 2, 8, 30WE, 36, 42, 46, 56WE, 60
• Content:
• vector versions of famous (simple) geometric constructions:
• the midpoint of a line segment
• the perpendicular bisector of a line segment
• the normal and general forms of the equation of a line in R2
• the vector form of the equation of a line in R2 or R3
• parametric equations for a line in R2 or R3
• W:
• Read: §1.3 (still)
• Content:
• the normal and general forms of the equation of a plane in R3
• the vector form of the equation of a plane in R3
• parametric equations for a plane in R3
• the distance from a point to a plane in R3
• F:
• Read: Exploration: The Cross Product, p. 45-46
• Content:
• the cross product of two vectors in R3
• the right-hand rule
• the geometric interpretation of the cross product

• M:
• Hand in MI2 and exercises HW2:
• §1.3: 2, 10, 14, 18, 20, 22WE, 24
• From Exploration: The Cross Product, p.46: 3WE
• Review Exercises, p. 56: 8, 10
• Content:
• a linear equation and systems of linear equations
• solutions of linear equations and linear systems
• equivalent linear systems
• the possible numbers of solutions of a linear system — the geometric viewpoint
• the coefficient and augmented matrix of a linear system
• solving a system by back substitution
• W:
• Read: §§2.1 (still) & 2.2 (but skip the part about Zp, on pp.80–82)
• Content:
• a matrix in row echelon form
• elementary row operations
• matrices which are row equivalent
• Gaussian elimination
• the rank of a matrix
• the Rank Theorem
• F:
• Read: §2.2 (still; continue to skip the part about Zp, on pp.80–82)
• Content:
• a matrix in reduced row echelon form
• Gaussian-Jordan elimination
• homogeneous systems

• M:
• W:
• More review for Test I
• Test I.A will take place today, which is the part covering linear systems [the material from §§2.1 & 2.2]
• F:
• Test I.B will take place today, on the basics of vectors and applications to lines and planes [the material we covered in Chapter 1]

• M:
• going over Test I.A
• Content:
• the span of some vectors in Rn; a spanning set
• linear [in]dependence of a set of vectors in Rn
• theorem relating the consistency of a non-homogeneous system to a condition on the span of the columns of the coefficient matrix
• W:
• going over Test I.B
• Read: §2.3 (still)
• Content:
• linear independence and rank
• linear independence of m vectors in Rn
• F:
• Read: §2.4 [particularly up through p.105]
• Content:
• generalities on word problems equivalent to linear systems
• balancing chemical equations, and other situations involving total consumption of limited resources
• flows in networks

• M:
• Read: §3.1 (but skip pp. 143–146, "Partitioned Matrices")
• Content:
• what is a matrix
• matrix equality; addition, subtraction, and the zero matrix; scalar multiplication
• matrix mutiplication: when it is defined, properties, the identity matrix
• the transpose of a matrix; symmetric matrices
• W:
• Hand in revised solutions to Test I.A&B problems for extra credit.
• Content:
• properties of matrix arithmetic operations, alone and in combination: analogues of the usual associative and distributive laws for numbers continue to apply ...
• ... but matrix multiplication is not commutative [herein lies the agony and the ecstasy of working with matrices!]
• F:
• Hand in MI4 and exercises HW4:
• §2.2: 39WE
• §2.3: 4, 8, 22, 26, 30, 34
• §2.4: 4WE, 16WE, 32WE
• Content:
• definition of the inverse of a matrix; an invertible matrix
• relevance of the inverse for solving linear systems
• properties of inverses and of the inversion operation

• M:
• going over Test II
• W:
• Read: §§3.3 & 4.1
• Content:
• more properties of inverses and of the inversion operation
• elementary matrices and invertibility
• the Fundamental Theorem of Invertible Matrices, version 1
• eigenvalue, eigenvector, and eigenspace
• F:
• Hand in revised solutions to Test II problems for extra credit.
• Read: §4.2 (not pp.273(bot)–280)
• Content:
• simplest examples of computations of eigenstuff — use that λ can be an eigenvalue for a matrix A only if A-λI is non-invertible
• definition of the determinant of a 2×2 and then 3×3 matrices
• the Laplace Expansion Formula
• first properties of determinants

• M:
• Read: §4.2 (not pp.273(bot)–280) (still)
• Hand in MI6 and exercises HW6:
• §3.3: 32, 36, 38, 40WE
• §4.1: 2, 6, 8, 12, 24WE, 37WE
• §4.2: 12, 14
• Content:
• more properties of the determinant
• Cramer's Rule
• W:
• Read: Exploration: Geometric Applications of Determinants, p. 283–288
• Content:
• determinants and the cross product
• areas of parallelgrams and volumes of parallelepipeds
• lines and planes
• curve fitting
• F:
• Read: §4.3 (ignore discussions of dimension and multiplicity)
• Content:
• the characteristic polynomial char(A) of a square matrix A
• a method to find eigenstuff with char(A)
• eigenstuff for triangular matrices
• the Fundamental Theorem of Invertible Matrices, version 2
• linear independence of eigenvectors corresponding to disctinct eigenvalues

 Jonathan Poritz (jonathan.poritz@gmail.com)