Description

Focuses on matrices, determinants, systems of equations, vector spaces including the four fundamental subspaces, orthogonality, inner product spaces, least square solutions, eigenvalues/eigenvectors, transformation matrices, dynamical systems and diagonalization. Geometrical understanding will be emphasized. Applications in business, computer science and engineering. Introduction to mathematical proofs.

Grading Basis

Graded

Prerequisites

MATH& 152 or Instructor Permission

### Course Learning Outcomes

### Core Topics

These should be topics that are the main body of the course. List topics so that other institutions should be able to identify what the course content is. List as optional any topics that may not be covered every quarter.

- Solving Systems of Equations using: Gaussian Elimination and Gauss-Jordan Elimination
- Applications of Systems of Linear Equations
- Operations with matrices particularly linear transformations.
- Vector spaces and subspaces
- Basis for the four fundamental subspaces of a matrix
- Invertible and Non-invertible matrices and their relationship to the four fundamental subspaces of a matrix.
- Matrix factorization including LU factorization, SBS-1, and SDS-1.
- Least square regression found by projecting a vector onto the image of A.
- Calculate and interpret determinants.
- Orthonormal basis
- Eigenvector and eigenvalue solutions to dynamical systems of linear equations.
- Optional: the use of linear algebra in solving systems of differential equations.
- Optional: Linear Transformations as related to calculus.