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Course: MATH 250, Fall 2008School: Rutgers
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8/26/04 Fall, revised 2004 640:250 Introduction to Linear Algebra Text: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Suggested Syllabus Lecture 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Reading 1.1, 1.2 1.3 1.4 1.6 1.7 1.7, 2.1 2.1 2.3 2.4 2.5 Topics Matrices and Vectors Systems...
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8/26/04
Fall, revised 2004
640:250 Introduction to Linear Algebra
Text: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458
Suggested Syllabus
Lecture 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 Reading 1.1, 1.2 1.3 1.4 1.6 1.7 1.7, 2.1 2.1 2.3 2.4 2.5 Topics Matrices and Vectors Systems of Linear Equations Gaussian Elimination Span of a Set of Vectors Linear Dependence and Linear Independence Homogeneous Systems, Matrix Multiplication Matrix Algebra Invertibility and Elementary Matrices Inverse of a Matrix LU Decomposition of a Matrix
Midterm Exam #1 3.1 3.2 4.1 4.2 5.1 4.3 5.2 5.3 5.5 Determinants; Cofactor Expansions Properties of Determinants Subspaces Basis and Dimension Column Space and Null Space of a Matrix Eigenvalues and Eigenvectors Characteristic Polynomial Diagonalization of a Matrix Applications of Eigenvalues (Markov Chains)
Midterm Exam # 2 6.1 Geometry of Vectors; Projection onto a Line 6.2 Orthogonal Sets of Vectors; Gram-Schmidt Process 6.2 Orthogonal Pro...
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Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/27/04Fall, 2004Math 250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4 1.6 1.7 2.1 2.
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #11 Revised 5/25/00LAB 1: Introduction to MATLABIn this lab you will learn how to use MATLAB to create and operate on matrices and vectors. The commands needed to do this are short and easy to remember, because MATL
Rutgers - MATH - 250
Math 250-CMATLAB Assignment #21 Revised 5/25/00LAB 2: Row Reduction and A = LU Matrix FactorizationIn this lab you will use MATLAB to obtain the A = LU factorization of an invertible square matrix (L unit lower triangular, U upper triangular).
Rutgers - MATH - 250
Math 250-CMATLAB Assignment #31 Revised 5/24/00LAB 3: Complete Solution to Ax = bIn this lab you will use MATLAB to study the complete solution of the linear equation Ax = b, where A is a given m n matrix, b is a given m 1 column vector and
Rutgers - MATH - 250
Math 250-CMATLAB Assignment #41 Revised 5/23/00LAB 4: Vector Spaces and Approximate Solutions to Ax = bIn this lab you will use MATLAB to study four topics: 1) The subspace spanned by a set of vectors, and the important concepts of independenc
Rutgers - MATH - 250
Math 250-CMATLAB Assignment #51 Revised 5/23/00LAB 5: A = QR Factorization, Determinants, and Eigenvalues/EigenvectorsIn this lab you will use MATLAB to study three topics: 1) How to transform a given set of basis vectors into an orthonormal b
Rutgers - MATH - 250
Math 250-CMATLAB Assignment #61 Revised 5/23/00LAB 6: Symmetric and Positive-Definite Matrices, Singular Value Decomposition, and Linear TransformationsIn this lab you will use MATLAB to transform a matrix into a diagonal matrix by finding its
Rutgers - MATH - 250
Intro. to Linear Algebra 250-C Extra Credit Project 1 - Graphs and Matrices Please write all answers on separate sheets of paper. Your answers should be numbered and in the same order in which the problems appear. Your project should be stapled and y
Rutgers - MATH - 250
Intro. to Linear Algebra 250-C Extra Credit Project 2 - Graphs and Markov Processes Introduction: In this project we will learn about the connection between linear algebra and market distribution. Suppose that, every day, there are three types of ent
Rutgers - MATH - 250
revised 8/27/04Fall, 2004640:250C Introduction to Linear Algebra General Information(MATLAB Sections)Text: Spence, Insel & Friedberg Elementary Linear algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 0745
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/27/04Fall, 2004640:250 Introduction to Linear Algebra(MATLAB Sections)Text: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458SyllabusLecture 1
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/27/04Fall, 2004Math 250-C Introduction to Linear Algebra with MATLABText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #11 Revised 9/15/02LAB 1: Matrix and Vector Computations in MATLABIn this lab you will use MATLAB to study the following topics: How to create matrices and vectors in MATLAB. The commands to do this are short and e
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #21 Revised 8/20/02LAB 2: Linear Equations and Matrix AlgebraIn this lab you will use MATLAB to study the following topics: Solving a system of linear equations by using the row reduced echelon form of the augmente
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #31 Revised 10/15/02LAB 3: LU Decomposition and DeterminantsIn this lab you will use MATLAB to study the following topics: The LU decomposition of an invertible square matrix A. How to use the LU decomposition to
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #41 Revised 10/25/02LAB 4: General Solution to Ax = bIn this lab you will use MATLAB to study the following topics: The column space Col(A) of a matrix A The null space Null(A) of a matrix A. Particular solutions
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #51 Revised 11/13/02LAB 5: Eigenvalues and EigenvectorsIn this lab you will use MATLAB to study these topics: The geometric meaning of eigenvalues and eigenvectors of a matrix Determination of eigenvalues and eige
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #61 Revised 11/11/02LAB 6: Orthonormal Bases, Orthogonal Projections, and Least SquaresIn this lab you will use MATLAB to study the following topics: Geometric aspects of vectors: the norm of a vector, the dot prod
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/21/06Fall, 2006640:250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458Suggested SyllabusLecture 1 2 3 4 5 6
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/21/06Fall, 2006Math 250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4 1.6 1.7 2.1 2.
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/19/03Fall, 2003640:250C Introduction to Linear Algebra General Information(MATLAB Sections)Text: Spence, Insel & Friedberg Elementary Linear algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 0745
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/9/03Fall, 2003640:250 Introduction to Linear Algebra (MATLAB Sections) Text: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-
Rutgers - MATH - 250
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Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 1/13/06Spring, 2006640:250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458Suggested SyllabusLecture 1 2 3 4 5
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 1/13/06Spring, 2006Math 250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4 1.6 1.7 2.1
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 1/10/05Spring, 2005640:250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458Suggested SyllabusLecture 1 2 3 4 5
Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 1/10/05Spring, 2005Math 250 Introduction to Linear AlgebraText: Spence, Insel & Friedberg Elementary Linear Algebra: A Matrix Approach ISBN # 0-13-716722-9, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4 1.6 1.7 2.1
Rutgers - MATH - 250
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Rutgers - MATH - 250
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Rutgers - MATH - 250
revised 8/24/01Fall, 2001640:250 Introduction to Linear AlgebraText: Kolman & Hill, Introductory Linear Algebra with Applications, 7th ed., ISBN # 0-13-018265-6, Prentice-Hall, Upper Saddle River, NJ 07458 Section 1.1 1.2 1.3 1.4 1.5 1.6 1.7 3.1
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #11 Revised 9/12/01LAB 1: Matrix Computations in MATLABIn this lab you will learn how to use MATLAB to create and operate on matrices and vectors. The commands needed to do this are short and easy to remember, becau
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #21 Revised 12/11/01LAB 2: Row Reduction and A = LU Matrix FactorizationIn this lab you will use MATLAB to obtain the A = LU factorization of an invertible square matrix (L unit lower triangular, U upper triangular)
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #31 Revised 12/12/01LAB 3: DeterminantsIn this lab you will use MATLAB to study the key aspects of the determinant of a square matrix: how it changes under row operations and matrix multiplication how it can be ca
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #41 Revised 12/11/01LAB 4: Vector Spaces and General Solution to Ax = bIn this lab you will use MATLAB to study the following topics: The subspace spanned by a set of vectors, and the fundamental concepts of indepe
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #51 Revised 12/12/01LAB 5: Orthogonal Subspaces, QR Factorization, and Inconsistent Linear SystemsIn this lab you will use MATLAB to study four topics: The Gram-Schmidt Algorithm that transforms a given set of basi
Rutgers - MATH - 250
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Rutgers - MATH - 250
Math 250-CMATLAB Assignment #61 Revised 12/12/01LAB 6: Eigenvalues and EigenvectorsIn this lab you will use MATLAB to study three topics: The geometric meaning of eigenvalues and eigenvectors of a matrix Determination of eigenvalues and eige