2-3 credits
Blue Book Description: Systems of linear equations appear everywhere in mathematics and its applications. MATH 220 will give students the basic tools necessary to analyze and understand such systems. The initial portion of the course teaches the fundamentals of solving linear systems. This requires the language and notation of matrices and fundamental techniques for working with matrices such as row and column operations, echelon form, and invertibility. The determinant of a matrix is also introduced; it gives a test for invertibility. In the second part of the course the key ideas of eigenvector and eigenvalue are developed. These allow one to analyze a complicated matrix problem into simpler components and appear in many disguises in physical problems. The course also introduces the concept of a vector space, a crucial element in future linear algebra courses. This course is completed by a wide variety of students across the university, including students majoring in engineering programs, the sciences, and mathematics. (In case of many of these students, MATH 220 is a required course in their degree program.)
Pre-requisites: Math 110 or 140
Pre-requisite for: Math 310, Math 484
Bachelor of Arts: Quantification
General Education: Quantification (GQ)
GenEd Learning Objective: Crit and Analytical Think
GenEd Learning Objective: Key Literacies
Suggested Textbook:
The Matrix Book by Pinaki Das. Open source textbook available here:
https://bpb-us-e1.wpmucdn.com/sites.psu.edu/dist/f/90663/files/2021/12/220Book.pdf
Check with your instructor to make sure this is the textbook used for your section.
Topics:
Chapter 1: Vectors, Lines and Planes
1.1 Vectors in R2 and R3
1.2 Vector Addition and Scalar Multiplication
1.3 Linear Equations in Two Variables
1.4 Linear Equations in Three Variables
Chapter 2: Gaussian Elimination
2.1 Row echelon form of a matrix
2.2 Linear systems of equations
2.3 Homogeneous Linear System of Equations
2.4 Reduced row echelon form of a matrix
Chapter 3: Matrices
3.1 Matrix Arithmetic
3.2 Matrix Product
3.3 Some Special Matrices
3.4 Elementary Matrices and Matrix Inverse
Chapter 4: Vector Spaces and Subspaces
4.1 Vector Spaces
4.2 Subspaces of a Vector Space
Chapter 5: Linear Independence, Basis and Dimension
5.1 Linear Combinations and Span
5.2 Linear Independence
5.3 Basis and Dimension
Chapter 6: The Four Fundamental Subspaces
6.1 Column and Row Spaces
6.2 Nullspace
6.3 Dimensions of the fundamental subspaces
Chapter 7: Linear Transformations
7.1 Linear Transformations Associated to Matrices
7.2 The Matrix of a Linear Transformation
Chapter 8: Determinants
8.1 Determinant of a 𝟐 × 𝟐 Matrix
8.2 Determinant of an 𝐧 × 𝐧 Matrix
8.3 Computing Determinants by Row Reductions
8.4 Minors and Cofactors
8.5 Inverse of a Matrix using Determinants
8.6 Cramer’s Rule
Chapter 9: Diagonalization
9.1 Eigenvalues and Eigenvectors
9.2 Diagonal Form of a Matrix
9.3 Applications
Chapter 10: Inner Products and Orthogonality
10.1 Inner Products
10.2 Orthogonality
10.3 Orthogonal Complements
10.4 Orthogonal Basis
10.5 Orthogonal Projections
10.6 Gram‐Schmidt Orthogonalization
10.7 Least Squares Estimation
Chapter 11: Orthogonal Matrices
11.1 Orthogonal Matrices
11.2 Orthogonal Diagonalization of Symmetric Matrices