An introduction to linear algebra: A curricular unit for pre-calculus students

Abstract

Matrices are important mathematical tools that facilitate the process of organizing and manipulating data. In this work, the matrix operations of addition, subtraction, scalar multiplication, and matrix multiplication are built logically from the intuition of the students and their knowledge of real numbers. From this knowledge, the concepts of inverses, determinants, and consistency and inconsistency of linear systems of equations are formed. Interesting applications of matrices in the areas of Markov chains, curve fitting, and eigenpairs are included and are not beyond the comprehension of pre-calculus students when they are presented carefully. Pre-calculus students can also appreciate many of the numerical challenges that can be encountered when real-world problems are solved; therefore, we include a discussion of some of these topics