LSC-CyFair Math Department
Matrices and linear systems, determinants, vector spaces, linear independence, basis and dimension, change of basis, linear transformations,similarity, inner product spaces, eigenvalues and
eigenvectors, and diagonalization. Applications of these concepts will also be considered.
Course Learning Outcomes
The student will:
Be able to solve systems of linear equations using multiple methods, including Gaussian elimination and matrix inversion.
Be able to carry out matrix operations, including inverses and determinants.
Demonstrate understanding of the concepts of vector space and subspace.
Demonstrate understanding of linear independence, span, and basis.
Be able to determine eigenvalues and eigenvectors and solve problems involving eigenvalues.
Apply principles of matrix algebra to linear transformations.
Demonstrate application of inner products and associated norms.
Construct proofs using definitions and basic theorems.
Contact Hour Information
Credit Hours: 3
Lecture Hours: 3
Lab Hours: 0
External Hours: 0
Total Contact Hours: 48
ENGL 0305 or ENGL 0365 OR higher level course (ENGL 1301), OR placement by testing
Textbook:DeFranza and Gadliardi; Introduction to Linear Algebra with Applications, 1st ed.; McGraw Hill; ISBN Numbers:
Calculator:Graphing Calculator required. TI 83, TI 84 or TI 86 series calculators recommended.
Chapter 1 Systems of Linear Equations and Matrices
1.1 Systems of Linear Equations
1.2 Matrices and Elementary Row Operations
1.3 Matrix Algebra
1.4 The Inverse of a Square Matrix
1.5 Matrix Equations
1.7 Elementary Matrices and LU Factorization
Chapter 2 Linear Combinations and Linear Independence
2.1 Vectors in Rn
2.2 Linear Combinations
2.3 Linear Independence
Chapter 3 Vector Spaces
3.1 Definition of a Vector Space
3.3 Basis and Dimension
3.4 Coordinates and Change of Basis
Chapter 4 Linear Transformations
4.1 Linear Transformations
4.2 The Null Space and Range
4.4 Matrix Representation of a Linear Transformation
Chapter 5 Eigenvalues and Eigenvectors
5.1 Eigenvalues and Eigenvectors
Chapter 6 Inner Product Spaces
6.1 The Dot Product on Rn
6.2 Inner Product Spaces
6.6 Diagonalization of Symmetric Matrices