Basic Technical Mathematics, 11th Edition

16.1 Matrices: Definitions and Basic Operations

• Elements of a Matrix • Square Matrix • Equality of Matrices • Matrix Addition and Subtraction • Scalar Multiplication

In this section, we introduce the definitions and some basic operations with matrices. In the three sections that follow, we develop additional operations and show how they are used in solving systems of linear equations.

A matrix is an ordered rectangular array of numbers. To distinguish such an array from a determinant, we enclose it within brackets. As with a determinant, the individual members are called elements of the matrix.

EXAMPLE 1 Illustrations of matrices

Some examples of matrices are shown here.

$$\begin{array}{l}\hspace{0.17em}[\hspace{0.17em}\begin{array}{rr}2& 8\\ 1& 0\end{array}\hspace{0.17em}]\hspace{0.17em}\hspace{0.17em}[\hspace{0.17em}\begin{array}{rrr}2& \hspace{0.17em}-\hspace{0.17em}4& 6\\ \hspace{0.17em}-\hspace{0.17em}1& 0& 5\end{array}\hspace{0.17em}]\hspace{0.17em}\hspace{0.17em}[\hspace{0.17em}\begin{array}{rr}4& 6\\ 0& \hspace{0.17em}-\hspace{0.17em}1\\ \hspace{0.17em}-\hspace{0.17em}2& 5\\ 3& 0\end{array}\hspace{0.17em}]\hspace{0.17em}\\ \hspace{0.17em}[\hspace{0.17em}\begin{array}{rrrrr}\hspace{0.17em}-\hspace{0.17em}1& 8& 6& 7& 9\\ 2& 6& 0& 4& 3\\ 5& \hspace{0.17em}-\hspace{0.17em}\; ...\end{array}\end{array}$$