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1.3 Rectangular arrays of real numbers arise in many contexts other than as
augmented matrices for systems of linear equations. In this section we begin
MATRICES AND MATRIX our study of matrix theory by giving some of the fundamental definitions of
the subject. We shall see how matrices can be combined through the
OPERATIONS arithmetic operations of addition, subtraction, and multiplication.
Matrix Notation and Terminology
In Section 1.2 we used rectangular arrays of numbers, called augmented matrices, to abbreviate systems of linear equations.
However, rectangular arrays of numbers occur in other contexts as well. For example, the following rectangular array with
three rows and seven columns might describe the number of hours that a student spent studying three subjects during a
certain week:
Mon. Tues. Wed. Thurs. Fri. Sat. Sun.
Math 232 4 14 2
History 0 3 1 4 32 2
Language 4 1 3 1 00 2
If we suppress the headings, then we are left with the following rectangular array of numbers with three rows and seven
columns, called a “matrix”:
More generally, we make the following definition.
DEFINITION
A matrix is a rectangular array of numbers. The numbers in the array are called the entries in the matrix.
EXAMPLE 1 Examples of Matrices
Some examples of matrices are
