MATH 2010 - Introduction to Linear Algebra
3 sem hrs cr
This course is a study of matrices, systems of linear equations, determinants, vectors, vector spaces, eigenvalues, eigenvectors, and other selected topics. Prerequisite: MATH 1910
In rare and unusual circumstances, a course prerequisite can be overridden with the permission of the Department Lead for the discipline.
Formerly/Same As (Formerly MAT 2830)
Transfer (UT) or Non-Transfer Course (UN): UT
Master Course Syllabus
Student Learning Outcomes
By the end of the course, students will be able to…
- teach the skills needed to solve systems of equations using various matrix methods.
- familiarize students with theoretical aspects of matrix operations, including proofs.
- teach skills needed to evaluate and use determinants.
- teach vector skills that are necessary in other academic courses.
- introduce the student to abstract mathematical thinking using the concept of a vector space.
- teach the student how to find and change bases of vector spaces.
- teach the student how to find eigenvectors and eigenvectors of a matrix.
- make the student familiar with certain applications of matrix theory.
Throughout the course, students will have the opportunity to…
- understand basic terminology and concepts regarding solutions of systems of linear equations.
- solve systems of linear equations using Gaussian elimination and Gauss-Jordan elimination.
- perform matrix operations, including addition, subtraction, multiplication, and transpose.
- use matrix operations to find the inverse of a matrix.
- understand algebraic properties of matrices.
- use elementary row operations to find the inverse of a matrix.
- perform operations with diagonal, triangular, and symmetric matrices.
- evaluate determinants of matrices by cofactor expansion.
- evaluate determinants of matrices by row reduction.
- use algebraic properties of determinants to solve problems.
- solve systems of linear equations using Cramer’s Rule.
- understand basic terminology and geometric and algebraic operations on vectors in 2, 3, and n dimensions.
- find the norm of a vector and perform vector arithmetic.
- find dot products of two vectors and the angle between two vectors and understand the geometric interpretation of the dot product.
- understand the idea of orthogonality and solve problems involving perpendicular vectors, including projections and distances.
- find the cross product of two vectors and apply to geometric problems.
- understand and verify the ten axioms of a vector space.
- recognize and verify when one vector space is a subspace of another.
- understand the concepts of linear independence and dependence of sets of vectors and spanning sets.
- find bases for vector spaces.
- find the dimension of a vector space and understand its algebraic and geometrical significance.
- change the basis of a vector space.
- find the row, column, and null vector spaces of a given matrix and understand their relationships to systems of linear equations. (optional)
- determine the rank of a matrix and understand its implications. (optional)
- find the eigenvalues and eigenvectors of certain matrices.
- understand Theorem 5.1.6, which ties together most of the main ideas of the study of the subject of linear algebra.
- define and be able to identify inner product spaces. (optional)
- construct an orthonormal basis for a vector space using the Gram-Schmidt process.
- solve systems of linear equations.
- recognize and apply orthogonal square matrices. (optional)
- understand general linear transformations and be able to perform them. (optional)