TABLE OF CONTENTS To discuss the solution of linear systems, it will be necessary to introduce the basic algebraic properties of matrices, which make it possible to describe linear systems in a concise way that make solving a system of n linear equations as easy as possible.
A matrix can be described as a rectangular array of elements that can be represented as follows:
The numbers a 11, a 12, , a mn that make up the array are called the elements of the matrix. The first subscript for the element denotes the row and the second denotes the column in which the element appears. The elements of a matrix may take many forms. They could be all numbers (real or complex), variables, functions, integrals, derivatives, or even matrices themselves.
The order or size of a matrix is specified by the number of rows (m) and columns (n); thus matrix A in (3.9) is of order m by n, usually written as m n.
A vector can be considered a special case of a matrix having only one row or one column. A row vector containing n elements is a 1 n matrix, called a row matrix, and a column vector of n elements is an n 1 matrix, called a column matrix. A matrix of order 1 1 is called a scalar.
Two matrices A=
