LINEAR ALGEBRA Penn State Bluebook - Penn State University

PENN STATE UNIVERSITY MATH 220: LINEAR ALGEBRA Penn State Bluebook: 1. Systems of Linear Equations 2. Matrix Algebra 3. Eigenvalues and Eigenvectors 4. Linear Systems of Differential Equations The above is taken from the Penn State bluebook. However, the members of the committee in Behrend feel that we should also include the part of linear algebra that includes “Abstract Vector spaces and subspaces with examples”. This outline will be different from all other courses because it remains a guideline (except the final exam policy which should be observed) and will have four books to choose from. All sections listed in the books MUST be covered and some sections with ** are only recommended. It is up to the initiatives of the professors to include other sections of the book. The four books chosen are: 1. Linear Algebra and Its Applications (4th Edition) by David C. Lay 2. Linear Algebra with Applications (8th Edition) by Steven J. Leon 3. Linear Algebra With Applications (Freeman) by Jeffrey Holt 4. Elementary Linear Algebra with Applications - 9th edition by Bernard Kolman and David R. Hill

Footnote: In a departmental meeting, we will push for “no exam on the last day of Week 10” and A cumulative final exam on the 11th week (2 different days chosen from M, W or F).

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Linear Algebra and Its Applications (4th Edition) by David C. Lay Chapter 1 Linear Equations in Linear Algebra 1.1 Systems of Linear Equations 1.2 Row Reduction and Echelon Forms 1.3 Vector Equations 1.4 The Matrix Equation Ax = b 1.5 Solution Sets of Linear Systems 1.6 Applications of Linear Systems ** 1.7 Linear Independence 1.8 Introduction to Linear Transformations 1.9 The Matrix of a Linear Transformation Chapter 2 Matrix Algebra 2.1 Matrix Operations 2.2 The Inverse of a Matrix 2.3 Characterizations of Invertible Matrices 2.7 Applications to Computer Graphics ** Chapter 3 Determinants 3.1 Introduction to Determinants 3.2 Properties of Determinants Chapter 4 Vector Spaces 4.1 Vector Spaces and Subspaces 4.2 Null Spaces, Column Spaces, and Linear Transformations 4.3 Linearly Independent Sets; Bases 4.5 The Dimension of a Vector Space 4.6 Rank Chapter 5 Eigenvectors and Eigenvalues 5.1 Eigenvectors and Eigenvalues 5.2 The Characteristic Equation 5.3 Diagonalization ** 5.7 Applications to Differential Equations

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Linear Algebra with Applications (8th Edition) by Steve Leon Chapter 1 Matrices and Systems of Equations 1.1 Systems of Linear Equations 1.2 Row Echelon Form 1.3 Matrix Arithmetic 1.4 Matrix Algebra Chapter 2 Determinants 2.1 The Determinant of a Matrix 2.2 Properties of Determinants Chapter 3 Vector Spaces 3.1 Definition and Examples 3.2 Subspaces 3.3 Linear Independence 3.4 Basis and Dimension 3.6 Row Space and Column Space Chapter 4 Linear Transformations 4.1 Definition and Examples 4.2 Matrix Representation Chapter 6 Eigenvalues 6.1 Eigenvalues and Eigenvectors 6.2 Systems of Linear Differential Equations 6.3 Diagonalization **

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Elementary Linear Algebra with Applications by David Hill Chapter 1 Linear Equations Matrices 1.1 Systems of Linear Equations 1.2 Matrices 1.3 Matrix Multiplication 1.4 Algebraic Properties of Matrix Operations 1.6 Matrix Transformation ** 1.7 Computer Graphics (optional) ** Chapter 2 Solving Linear Systems 2.1 Echelon Form of a Matrix 2.2 Solving Linear Systems 2.3 Elementary Matrices; Finding inverse of A Chapter 3 Determinants 3.1 Definition 3.2 Properties of Determinants Chapter 4 Real Vector Spaces 4.1 Vectors in the Plane and in 3-Space 4.2 Vector Spaces 4.3 Subspaces 4.4 Span 4.5 Linear Independence 4.6 Basis and Dimension 4.7 Homogeneous Systems 4.9 Rank of a Matrix Chapter 7 Eigenvalues and Eigenvectors 7.1 Eigenvalues and Eigenvectors Chapter 8 Applications of Eigenvalues and Eigenvectors 8.4 Differential Equations

Note: Hill’s book tend to have too much and cover more than what we need especially in Chapter 4. It is up to the instructor discretion to cover parts of the sections in Chapter 4 as long as it adheres to what is in the blue book. 4

Linear Algebra with Applications by Jeffrey Holt Chapter 1 Systems of Linear Equations 1.1 Lines and Linear Equations 1.2 Linear Systems and Matrices 1.4 Applications of Linear Systems ** Chapter 2 Euclidean Space 2.1 Vectors 2.2 Span 2.3 Linear Independence Chapter 3 Matrices 3.1 Linear Transformations 3.2 Matrix Algebra 3.3 Inverses Chapter 4 Subspaces 4.1 Introduction to Subspaces 4.2 Basis and Dimension 4.3 Row and Column Spaces Chapter 5 Determinants 5.1 The Determinant Function 5.2 Properties of Determinants Chapter 6 Eigenvalues and Eigenvectors 6.1 Eigenvalues and Eigenvectors 6.5 Complex Eigenvalues ** 6.6 Systems of Differential Equations

Note: In the meeting for this syllabi, this book is considered the best alternative to Lay’s new edition. 5