Elementary Linear Algebra
 Course: MAT225 First Term: 2004 Spring Final Term: Current Final Term: 2020 Spring Lecture   3.0 Credit(s)   3.0 Period(s)   3.0 Load       Credit(s)    Period(s)    Load Subject Type: Academic Load Formula: S

Description: Introduction to matrices, systems of linear equations, determinants, vector spaces, linear transformations and eigenvalues. Emphasizes the development of computational skills.

MCCCD Official Course Competencies
1. Analyze the existence and character of the solution(s) of a system of linear equations using a rowechelon form of the augmented matrix determinant. (I, II)
2. Display knowledge of matrix and determinant operations and properties. (I, II)
3. Use the Euclidean inner product and other inner products to define length and distance for vector spaces. (III)
4. Determine whether a set of vectors is a vector space and whether a subser of vectors is a subspace. (III)
5. Determine a basis for a vector space. (III)
6. Use the Gram-Schmidt process to obtain an orthonormal basis for an inner product space. (III)
7. Determine bases for the row space, column space, null space and possible eigenspaces of a matrix A. (III, IV)
8. Determine whether a transformation T is linear and find bases for the kernel and range of T. (V)
9. Use current technology to solve problems in the context of the course. (I, II, III, IV, V)

MCCCD Official Course Outline
I. Linear Equations and Matrices
A. Linear Systems
1. Methods of elimination
2. Dependent and inconsistent systems
B. Matrices
1. Operations on matrices
2. Properties of matrix operations
3. Inverse of a matrix
4. Solutions of equations using matrices
II. Determinants
A. Definitions and properties
B. Cofactor expension
III. Vectors and Vector Spaces
A. Vectors in R2 and R3
1. Vector operations
2. Orthogonal and unit vectors
B. Vectors in Rn
1. Inner product
2. Triangle inequality
C. Vector spaces and subspaces
1. Properties of vector spaces
2. Definition of a subspace
3. Span of a set of vectors
D. Linear independence
E. Basis and dimension
1. Definition of a basis
2. Finite and infinite - dimensional vector spaces
F. Rank of a matrix
1. Row rank and column rank
2. Consistency of non homogeneous linear systems
G. Orthonormal basis in Rn (Gram-Schmidt process)
IV. Eigenvalues and Eigenvectors
A. Characteristic polynomials and equations for square matrices
B. Determining eigenvalues and eigenvectors for a square matix
C. Diagonalization of a matrix
V. Linear Transformations and Matrices
A. Properties and examples of linear transformations
B. Kernel and range of a linear transformation
C. Matrix of a linear transformation

MCCCD Governing Board Approval Date: 6/25/1995

All information published is subject to change without notice. Every effort has been made to ensure the accuracy of information presented, but based on the dynamic nature of the curricular process, course and program information is subject to change in order to reflect the most current information available.