Technical Mathematics, Sixth Edition

10.1. Introduction to Matrices

10.1.1. Arrays

A set of numbers, called elements, arranged in a pattern, is called an array. Arrays are named for the shape of the pattern made by the elements.

Example 1: square array rectangular array triangular array

In everyday language, an array is called a table.

10.1.2. Matrices

A matrix is a rectangular array.

Example 2: In Example 1, (a) and (b) are matrices. Further, (a) is a square matrix. For a square matrix, the diagonal running from the upper-left element to the lower-right element is called the main diagonal. In (a), the elements on the main diagonal are 3, 3, and 4. The diagonal from upper right to lower left is called the secondary diagonal. In our example, the elements 4, 3, and 9 are on the secondary diagonal.

10.1.3. Subscripts

Each element in an array is located in a horizontal row and a vertical column. We indicate the row and column by means of subscripts.

Example 3: The element a25 is located in row 2 and column 5.

Thus an element in an array needs double subscripts to give its location.

CLASS PROBLEM: Determine the dimensions of the following matrices: (5 6 3) ANSWER: 2 × 3 1 × 3 3 × 1

10.1.4. Dimensions

A matrix will ...