This volume is an experimental edition for a high school course in the theory of matrices and vectors. One of the basic aims is to demonstrate the structure of mathematics. Another criterion is to provide some tools that will be useful in the student's transition from school to college. A last objective is that the intellectually vigorous students may obtain an idea of what constitutes "mathematical research." The five chapters found in the text are: (1) Matrix Operations; (2) The Algebra of 2x2 Matrices; (3) Matrices and Systems of Linear Equations; (4) The Representation of Column Matrices as Geometric Vectors; and (5) Transformations of the Plane. Research Exercises are also included. (Author/MK)