## Matrices

### Course Description

Many problems we have to solve in day-to-day business, engineering, and science practice require the simultaneous study of several different but interrelated factors. Although problems of this form have been studied throughout the long history of mathematics, only in the early 20th century did the systematic approach we now refer to as linear algebra based on matrices emerge. Matrices and linear algebra are now recognized as the fundamental tool for foundational methods in statistics, optimization, quantum mechanics, and many other fields, and are an essential component of most subfields of mathematics. Linear algebra provides students their first introduction to the concept of dimension in an abstract setting where things with 4, 5, or even more dimensions are often encountered.

MATH 220 is a 2 credit course that teaches the core concepts of matrix arithmetic and linear algebra. It is a required course for many students majoring in engineering, science, or secondary education. In past coursework, students should have gained practice solving pairs of equations like 3 x + 4 y = 10, x - y = 1. This is a system of two linear equations with two unknowns and as a unique solution students can find by isolating and substituting. In linear algebra, this system is represented as A x = b, where x is a vector of unknowns, A is a matrix, and b is a vector of constants. Linear algebra is the field of mathematics that grew out of a need to solve systems like these and related problems with many unknown variables.

Topics covered in MATH 220 include matrix algebra, vectors, linear transformations, solution to systems of linear equations, determinants, matrix inverses, concepts of rank and dimension, eigenvalues, eigenvectors, and others as time permits. Course prerequisites can be filled by one semester of calculus. Students may take MATH 220 concurrently with MATH 141, MATH 230, or MATH 250. Students seeking a linear algebra course without a calculus prerequisite may consider MATH 018 as an alternative. After completing MATH 220, students can enroll in MATH 441 or MATH 484. MATH 441 provides more in-depth perspective on linear algebra. MATH 484 studies widely used applications of linear algebra to optimization problems.

Class size, frequency of offering, and evaluation methods will vary by location and instructor. For these details check the specific course syllabus.

An honors version of this course is offered at least once per year.

**Sample Final Exams**