Matrices and Matrix Algebra

This chapter introduces basic notation, matrix algebra, and processes associated with matrices. After establishing notation, the chapter continues with row operations and Gauss-Jordan elimination. Reduced echelon form is defined, and students practice these processes in the associated software. Addition and multiplication of matrices are introduced, which also may be practiced in the software. Properties of these operations, such as the associative and distributive laws are established, with an emphasis on the lack of commutativity of matrix multiplication. Lack of commutativity is illustrated via rotations in space. The chapter concludes with a thorough discussion of matrix inverses, along with an algorithm for finding inverses, which may be practiced in the software.