MAC/IPAD/IPhone-Compatible Online Video Lectures for Linear Algebra, MATH 3328/2318, Summer 2012

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Go to The Start of Linear Algebra Lectures then scroll down to the current lecture.

General Infomation
1) Home work assignment
2) Course Information for MATH 3328
3) Text: Elementary Linear Algebra with Applications, 3rd Edition, by Richard Hill, ISBN 0030103479.
Available at bookstores as well as online, such as
Amazon Barnes and Noble Ebay Abebooks

Home work:
At a minimum, do the problems listed on the homework sheet given at the beginning of the semester.
Follow the methods used in class or shown in the text book.
Compare your final answer with the solution to the odd-numbered problems at the end of the text.
Form study groups.
Use free tutoring available in L209, M-R 8-6, F 8-2. Talk to several tutors. Ask questions collectively.
Bring up your un-answered questions in office hours.
Or bring up your un-answered questions in class.

How to help yourself get ready for tests:
Give yourself self-tests: Write problems (whose solutions you have seen) on a flash card. Indicate where solution can be found and allocated time. Store in a box. Draw 10 random questions, give yourself a timed test. Grade using the available solutions. Re-study problems you missed.
In case we use the hybrid approach you want to make sure your your lecture note and homework binder is complete, searchable and readable to yourself.

Restriction/Policy regarding notebooks and calculators
Only one binder note-book of your own hand-written items is allowed on tests.
No printed paper allowed. No copied paper allowed. This will result in a grade of F for the course even if not used!
No type of loose paper of any form is allowed on tests. No torn/glued/stapled/sewn/stitched paper allowed.
You may have a regular basic scientific calculator (about $20) on tests. Use of advanced calculators (such as TI80 etc) will result in a grade of F for the test.
No wireless devices allowed. No cell-phone/ipod-style calculator allowed.
If you do not have your own proper calculator then you will take your test without one.


Extras:
Online Courses, Texts, Interactive Calculators, Simulators, Games, and Demos Related to Linear Algebra:
Linear Algebra by Gilbert Strang a complete course package. You may also use 1999 version.
Linear Algebra Course by Alex Postnikov, 2009
Matrix analysis and applied linear algebra Text by Carl D. Meyer.
Introduction to matrix algebra Text by Autar K. kaw.
Linear Algebra Text by Jim Hefferon. Large PDF Download.
How to speed up the video replay.
Interactive Apps
Linear Algebra Toolkit Calculator by Przemyslaw Bogacki, Old Dominion University
Basic Matrix algebra Calculator for multiplication, determinant, inverse, Gussian elimination or rref (row reduction to echelon form).
Step-by-Step ow Operations
3D plots
Games
Lights Out 1 , By David Guichard, Whitman College, A linear algebra game somewhat similar to the classical Othello/Reversi game, but single player. Can you find out how to solve the Lights Out puzzle by applying linear algebra?
Lights out 2, by Misha Guysinski, at Penn State.
Fifteen , by Misha Guysinski, at Penn State. This one requires permutations.


Start of Linear Algebra Lectures:
Read Section 1.1 Pages 1-3
Do problesm from 1-20.
Lecture 1, Introduction
linear equations, a solution, solving, solution set, parametric solution, system of linear equations, linear systems, inconsistent systems, consistent systems, graphical solution, a linear system may have 0 or 1 or infinitely many solutions.

Read Section 1.1 Pages 4-9
Do problems from 21-32.
Lecture 2, Introduction
Motivation for studying linear algebra, Gaussian elimination, triangular form, echeleon form, backsubstitution, coefficient matrix, augmented matrix, right hand side column, elementary operations on a linear system, elementary row operations on a matrix.

Extras: To check your elementary row operations you may try this calculator, click on the first tool link "Row Operation Calculator" on the page.
Matrix Toolkit
If you want to SEE how a certain formula with up to three variables looks use the following interactive page/applet/app:
3D plots

Read Section 1.2 Pages 10-13.
Do problesm from 1-14.
Lecture 3, Gaussian Elimination
parametric equations and deciding 0, 1, or infinitely many solutions, echelon form, leading zeros, pivot elements, leading/dependent variables, free/independent variables, how to solve an equation given in echelon matrix form.

Read Section 1.2 Pages 13-21.
Do problems from 15-29.
Lecture 4, Gaussian Elimination
Elementary row operations used to reduce an equation to its echelon form; so that it can be solved by back-substitution.

To check your echelon form or to solve your system you may try this calculator (use the 2nd or 4th tool).
Matrix Toolkit

Read Section 1.3 Pages 23-27
Do problems from 1-14.
Lecture 5, Matrix Algebra
Problem 15 from 1.2, matrix entry or element, matrix size or dimension, double subscript, matrix addition and subtraction, scalars and matrices, multiplication of a scalar and a matrix, dot product or inner product, matrix product as a collection of dot products.

To check your mutiplication try this calculator
Basic Matrix algebra
To see
demo of multiplication search for "work out", click on "multiply two matrices", follow directions.

Read Section 1.3 Pages 27-29
Do problems from 15-16.
Lecture 6, Matrix multiplication
more on matrix product as a collection of dot products, general formula using summation notation

To check your mutiplication try this calculator
Basic Matrix algebra
To see
demo of multiplication search for "work out", click on "multiply two matrices", follow directions.

Read Section 1.3 Pages 30-31
Do problems from 21-26, try 27-32, especially 31, skip 17-20.
Lecture 7, Interpretations of Matrix multiplication
multiplication by a diagonal matrix, a linear system written as matrix product, substitution as matrix multiplication, matrix multiplication as a sum of products of columns with rows.

Read Section 1.3 Pages 32-34, 1.4 Pages 38-39
Do problems from 1.3, 33-42. At least one from each type even though not on the blue page list!
Lecture 8, Different styles for Matrix multiplication
Interpretations of A.B in terms of dot products of rows of A with columns of B, A with columns of B, rows of A with B, row matrices of A with column matrices of B, sum of outer products of columns of A with corresponding rows of B. AX, X a vector, is the linear combination of columns of A with weights same as entries of vector X.

Read Section 1.4 Pages 38-45
Do problems from 1,3,5,8,10,11,14.
Lecture 9, Inverses and elementary matrices
Elemetary matrix associated with multiplication of a row and exchange of two rows.

Read Section 1.4 Pages 38-45
Do problems from 1-24, 36, 39, 40, 41-43, 45, 49, 50 .
Lecture 10, Inverses and elementary matrices
Elementary COLUMN operations (related to problem 50).
Problem 37 from 1.3, different styles (row expansion, column expansion, outer product expansion) for multiplication of matrices, related to lecure 8.
Elemetary matrix associated with adding multiple of a row to another row.
General procedure for finding the inverse.

Read Section 1.4 Pages 48-49
Do problems from 9-20, 25-45.
Lecture 11, Finding Inverses using elementary matrices
An example of 3*3 matrix being inverted. Short discussion of non-invertible matrices.

Read Section 1.5 Pages 57-64
Do problems from 1-8.
Lecture 12, LU factorization
LU factorization for a simplae case (without permutatio), description of algorithm and justification of procedure.

Read Section 1.5 Pages 62-64.
Do problems from 9-24.
Lecture 13, Solving AX=B via LU factorization
Advantages of LU factorization, solving systems with factorization, general permutation matrices, PA=LU.

Read Section 1.5 Pages 64-67, 1.6 Pages 71-72, 3.1 Pages 130-131
Do problems from 1.5 33-36, from 1.6 1-7, 13,14,19,20.
Lecture 14, Solving AX=B via PA=LU factorization,
an example, symmetric, skew-symmteric, determinants of 2*2 and 3*3 matrices, vectors in physics

Read Section 3.1 Pages 132-137, 151
Do problems from 3.1, 1-30 (postpone "span" questions)
Lecture 15, Vectors
scalars, vectors, matrices, graphical addition, subtraction, and scalar multiplication of vectors


Read Section 3.1 Pages 132-141
Do problems from 3.1, 1-36
Lecture 16, length and dot product of vectors
span, distance, norm (length, magnitude, size) of a vector, angle between vectors, dot product through angle, length interm of dot product, dot product in terms of components, example: find the angle between two vectors.


Read Section 3.1 Pages 140-144
Do problems from 3.1, 31-42
Lecture 17, Dot Product theorem, Projections
Example 5,11,36. Proof of Law of Cosines, Proof of U.V= u1 v1+ u2 v2 + u3 v3 = |U| |V| cos of angle. Formula for projections

Read Section 3.1 Pages 144-146
Do problems from 3.1, 43-50
Lecture 18, Gram-Schmidt Process
Example 21. Producing a set of mutually perpendicular vectors P_i out an arbitrary given Vectors V_i using projections.

Read Section 3.2 and 3.3 Pages 149-165
Do problems from 3.2, 3.3 all
Lecture 19, Euclidean n-Space, General Vector Spaces
Closure.
Review Section 1.4,1.5,1.6,3.1,3.2
Lecture 20, Review of Inverse, LU, PA=LU
A biref review.

Read Section 3.4 Pages 165-169
Do problems from 3.4, 1-24
Lecture 21, Subspaces
Closure with respect to vector addition and scalar multiplication.

Read Section 3.4 Pages 168-169
Do problems from 3.4, 1-24
Lecture 22, Subspaces
examples of subspaces

Read Section 3.4 Pages 169-173
Do problems from 3.4, 33-40
Lecture 23, Subspaces
Null spaces, NS(A), linear combinations

Read Section 3.4 Pages 173-176, 3.5 179-180
Do problems from 3.4, 41-48, 3.5 1-3
Lecture 24, Subspaces
linear combinations, interpretation of AX=B, linear dependence and independence

Read Section 3.5 Pages 179-180
Do problems from 3.5 1-6
Lecture 25, Linear Independence
Problems 29 and 38 from 3.4, Intro to linear dependence and independence

Read Section 3.5 Pages 180-185
Do problems from 3.5 7-24
Lecture 26, Linear Independence
linear dependence and independence

Read Section 3.6 Pages 187-192
Do problems from 3.6 1-20
Lecture 27a, Basis
Given a set of vectors how do we detect if they are a basis for a given space?
Lecture 27b, Basis, problem 13 Page 197

Lecture 27c, Basis, using dimension argument


Read Section 5.1 Pages 320-326
Do problems from 5.1 1-20
Lecture 28, Determinants
Introduction to determinants, short cuts, expansion/recursive formula

Read Section 5.1 Pages 326-329
Do problems from 5.1 21-39
Lecture 29, Determinants
Examples, three theorems.

Read Section 5.2 Pages 331-334
Do problems from 5.2 1-9, part b only of 11-22
Lecture 30, Introduction to Eigenvalues and Eigenvectors
Examples, Definitions.

Read Section 5.2 Pages 331-335
Do problems from 5.2 1-9, only part a,b of 11-22
Lecture 31, real, complex, double eigenvalues, characteristic polynomial of a matrix
several examples.

Read Section 5.2 Pages 331-335
Do problems from 5.2 1-9, only part a,b,c of 11-22
Lecture 32, Finding eigenvectors of a matrix, matrix factorization into eigenvector matrix *eigenvalue matrix* inverse of eigenvector matrix
several examples.

Read Section 5.2 Pages 331-335
Do problems from 5.2 18
Lecture 33, Finding eigenvectors of a 3*3 matrix,
One example.

Read Section 5.2 Pages 331-335
Do problems from 5.2 17-22
Lecture 34, Finding eigenvectors of a 3*3 matrix, diagonalization: matrix factorization into eigenvector matrix *eigenvalue matrix* inverse of eigenvector matrix f(A)= V f(lambda) V^ -1, several examples.

Read Section 5.2 Pages 331-335
Do problems from 5.2 17-22
Lecture 35, Repeated eigenvalues Finding eigenvectors and basis of eigenspaces for repeated roots of characteristic polynomial, several examples.

Read Section 5.2, Pages 338-339, 5.3 342-349
Do problems from 5.2 part (f) of 11-22, 5.3 1-26
Lecture 36, trace, determinants, and eigenvalues, diagonalizability sum of eigenvalues=trace, product of eigenvalues=determinant, f(A)=V f(lambda) V^-1

Read Section 5.3 342-349
Do problems from 5.3 1-26
Lecture 37, Diagonalization
Examples, non-diagonalizable matrices.

Read Section 5.4 352-358
Do problems from 5.4 1-9
Lecture 38, Symmetric Matrices
Properties, Orthogonal (Orthonormal) matrices, Theorem: Eigenvalues of a real symmetric 2*2 matrix are real.

Read Section 5.4 352-358
Do problems from 5.4 1-9
Lecture 39, Review of Symmetric Matrices
Solution of problem 1

Lecture 40, Partial Review of eigenvalues, eigenvectors, diagonalization, solution of a system of diff eq Covers parts of 5.2,5.3,5.6 (for 5.6 use lecture note)
Read second part of Section 5.5 352-358
Do problems from video
Lecture 41, Markov Processes, an example

Lecture 43, Basis a problem