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
"17_{WE}", 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*

(at jonathan.poritz@gmail.com) telling me:**HW0: Send me e-mail**- Your name.
- 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.)
- Your year/program/major at CSUP.
- The reason you are taking this course.
- What you intend to do after CSUP, in so far as you have an idea.
- Past math classes you've had.
- Other math and science classes you are taking this term, and others you intend to take in coming terms.
- Your favorite mathematical subject.
- Your favorite mathematical result/theorem/technique/example/problem.
- Anything else you think I should know (disabilities, employment
or other things that take a lot of time,
*etc.*) - [Optional:] The best book you have read recently.

*W:***Read:**§§1.1 & 1.2*Content:**scalar multiplication**vector addition*- properties of these vector operations
- the
*norm*of a vector - the
*dot product*of two vectors ,**R**^{2}, and**R**^{3}**R**^{n}- a
*linear combination*of two vectors *unit vectors*

*F:***Today [Friday] is the last day to add classes.****Read:**§1.2*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, 30
_{WE}, 36, 42, 46, 56_{WE}, 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**R**^{2} - the
*vector form of the equation of a line*inor**R**^{2}**R**^{3} *parametric equations*for a line inor**R**^{2}**R**^{3}

- vector versions of famous (simple) geometric constructions:

*W:***Read:**§1.3 (still)*Content:*- the
*normal*and*general forms of the equation of a plane*in**R**^{3} - the
*vector form of the equation of a plane*in**R**^{3} *parametric equations*for a plane in**R**^{3}- the distance from a point to a plane in
**R**^{3}

- the

*F:***Read:***Exploration: The Cross Product, p. 45-46**Content:*- the
*cross product*of two vectors in**R**^{3} - the
*right-hand rule* - the geometric interpretation of the cross product

- the

*M:***Read:**§2.1*Hand in***MI2**and exercises**HW2:**- §1.3: 2, 10, 14, 18, 20,
22
_{WE}, 24 - From
*Exploration: The Cross Product*, p.46: 3_{WE} - Review Exercises, p. 56: 8, 10

- §1.3: 2, 10, 14, 18, 20,
22
*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*

- a

*W:***Read:**§§2.1 (still) & 2.2 (but skip the part about, on pp.80–82)**Z**_{p}*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*

- a matrix in

*F:***Read:**§2.2 (still; continue to skip the part about, on pp.80–82)**Z**_{p}*Content:*- a matrix in
*reduced row echelon form* *Gaussian-Jordan elimination**homogeneous*systems

- a matrix in

*M:**Hand in***MI3**and exercises**HW3:**- §2.1: 6, 18, 22, 28, 32,
34
_{WE} - §2.2: 6, 8, 14, 32, 38,
40
_{WE}

- §2.1: 6, 18, 22, 28, 32,
34
- Starting review for Test I
- Here is a review sheet for the first midterm test.

*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:***Read:**§2.3- going over
**Test I.A** *Content:*- the
*span*of some vectors in; a**R**^{n}*spanning set* *linear [in]dependence*of a set of vectors in**R**^{n}- theorem relating the consistency of a non-homogeneous system to a condition on the span of the columns of the coefficient matrix

- the

*W:*- going over
**Test I.B** **Read:**§2.3 (still)*Content:*- linear independence and rank
- linear independence of
*m*vectors in**R**^{n}

- going over
*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*

- what is a

*W:**Hand in revised solutions to***Test I.A&B**problems for extra credit.**Read:**§3.2*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:***Read:**§3.3*Hand in***MI4**and exercises**HW4:**- §2.2: 39
_{WE} - §2.3: 4, 8, 22, 26, 30, 34
- §2.4: 4
_{WE}, 16_{WE}, 32_{WE}

- §2.2: 39
*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

- definition of the

*M:***Read:**§3.3 (still)*Content:*- revisit what is a matrix inverse, and how knowing one will help solving linear systems
- inverses for
*2×2*matrices — when they exist, a formula which computes them - the
*Gauss-Jordan*method of inverting a matrix

*W:**Hand in***MI5**and exercises**HW5:**- §3.1: 10, 12, 16, 18, 22
36
_{WE} - §3.2: 4, 26,
38
_{WE} - §3.3: 4, 12, 22

- §3.1: 10, 12, 16, 18, 22
36
- going over
**HW4**and**HW5** - Review for Test II
- Here is a review sheet for the second midterm test.
**Test II, Takehome Part**will be handed out today

*F:***Test II, Takehome Part**is due today,**in class****Test II, In-class Part, will take place today**

*M:*- going over
**Test II**

- going over
*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

- simplest examples of computations of eigenstuff — use that

*M:***Read:**§4.2 (**not**pp.273(bot)–280) (still)*Hand in***MI6**and exercises**HW6:**- §3.3: 32, 36, 38, 40
_{WE} - §4.1: 2, 6, 8, 12,
24
_{WE}, 37_{WE} - §4.2: 12, 14

- §3.3: 32, 36, 38, 40
*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

- the

- Last week of meeting for this course.
*M:**Hand in***MI7**and exercises**HW7:**- §4.2: 32, 34, 46
_{WE} - From
*Exploration: Geometric Applications of Determinants*, p.283: 1(a)&(b), 6, 11, 12_{WE}, 15 - §4.3: 2(a)&(b), 6(a)&(b), 10(a)&(b), 12(a)&(b),
17
_{WE}, 18_{WE},

- §4.2: 32, 34, 46
- Final review. Here is a review sheet for the material from Chapters 3 and 4 (so, the material since the second midterm); this should be consulted along side the reviews for Midterm I and Midterm II.

*W:***Final exam, part I**This part of the final will focus mostly on the more recent material, from around the time of the second midterm to the end of the course.

*F:***Final exam, part II**This part of the final will be more of mini-comprehensive-final, in that it will be fairly evenly divided into problems relating to all parts of the course.

Jonathan Poritz (jonathan.poritz@gmail.com) |