Catalog Description: Linear equations, matrices, linear transformations, eiganvalues, diagonalization, applications.
Total Credits: 3
Contact Hours: 3 lecture hours per week
Course Coordinator: Alexander Woo, Jennifer Johnson-Leung, Hong Wang, Mark J. Neilson
Prereq: MATH 175: Calculus II
Textbook: "Linear Algebra and Its Applications," 4th Edition, David C. Lay
Prerequisites by Topic:
Main Topics Covered
- Linear Equations
- Matrix Algebra
- Vector Spaces
- Eiganvalues and Eiganvectors
- Orthonganality and Least Squares
- Symmetric Matrices and Quadratic Forms
- The student will become better at reasoning with abstract ideas in a quantitative context. In particular, the student will learn to determine if particular examples satisfy a mathematical definition and to construct simple examples and non-examples to mathematical definitions.
- The student will understand and use standard linear algebra concepts, including vector spaces, subspaces, spanning sets, linear independence, basis, dimension, change of coordinates, standard matrix operations, null and column spaces of a matrix, rank, linear transformations, eiganvalues, eiganvectors, inner product spaces, and orthogonality. The student will understand and use the relationships between these concepts.
- The student will learn to perform the following procedures and understand why these procedures produce the desired answers.
- Compute the solution set to a linear system by using Gaussian elimination to bring the augmented matrix to reduced echelon form, then using the reduced echelon form to write the solution set in parametric vector form.
- Perform Standard matrix operations including addition, multiplication, and finding the inverse.
- Determine the eiganvalues of a matrix using the characteristic equation and find the eigenspace corresponding to a given eiganvalue.
- Compute the coordinates of a vector and the matrix of a linear transformation with respect to different bases.
- Generate an orthogonal basis for a given space.
- The student will improve their ability to communicate clearly, effectively, and in a organized fashion their reasoning, their understanding of concepts and their relationships to each other, and their understanding of procedures and their justification.