From the Preface:
This book is an introduction to linear algebra for pre-calculus students. It is a stand-alone unit in the sense that no prior knowledge of matrices is assumed. Students with experience in general mathematics, up to and including Algebra I, should be able to comprehend the material. However, most students have not had experience with the topics in the latter chapters, so the pace of the course should allow for the students to spend extra time with these chapters.
We begin with chapters that explain the matrix operations of addition, subtraction, scalar multiplication, and matrix multiplication. These topics are covered in most pre-calculus texts that are currently in use. This unit also allows the students to explore the notions of inverse, determinant, and consistent and inconsistent systems; these topics are covered in some pre-calculus text books. Our unit also provides the students with an introduction to Markov chains, curve fitting, eigenpairs, and some of the numerical challenges that are encountered when matrices are used to solve real-world problems. These latter topics are rarely addressed in pre-calculus texts. The unit was created from elementary principles with significant input from Rice University
faculty and students. Various current texts, recommendations from the National Council of Teachers of Mathematics
(NCTM), and the Texas Essential Knowledge and Skills
(TEKS) were examined in order to determine which topics should and should not be included in this text.
Because many books teach procedures rather than concepts, the students do not receive enough information to expand beyond the examples in the book. For example, some books teach methods which apply only to the special case of 2 by 2 matrices when they address the notions of inverse and determinant. However, this text presents methods for finding inverses and determinants of square matrices of any size. Since the students learn the concepts and these general methods, their knowledge is not restricted by the examples in the book.
This entire unit was written so that pre-calculus teachers and students will have a text that clearly and accurately explains the introductory concepts of linear algebra. It explores the topics that are currently addressed in pre-calculus courses, but emphasizes concepts rather than than just procedures. This unit also provides students with many more real-world linear algebra topics to explore than are presented in current texts. It is hoped that this unit will not only help students understand linear algebra, but will also spark an interest in, and an appreciation for, the mathematical sciences.