## Abstract

A matrix is a rectangular array of numbers arranged in rows and columns. As we shall see, a matrix is a convenient device for organizing data that would otherwise require several pages. In addition, many mathematical problems can be expressed much more concisely and solved much more easily using matrix notation and matrix operations. For example, a system of 10 linear equations with 10 unknowns can be expressed as a simple matrix equation *A*·*X*=*B*, and solved by a matrix equation *X*=*A*^{−1}·*B*. For reasons such as these, matrix algebra has become a required topic for students of business administration and many branches of science and engineering. In this chapter, we will concern ourselves with some of the basic theory of matrix algebra and explore the use of APL in working with vectors and matrices. In the next two chapters, we will consider some applications of matrices. As we shall see, APL is very well suited for handling arrays such as vectors and matrices.

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