Algebra and Trigonometry, 5th Edition

9.3 Matrices and Systems of Equations

• Solve systems of equations using matrices.

Matrices and Row-Equivalent Operations

In this section, we consider additional techniques for solving systems of equations. You have probably observed that when we solve a system of equations, we perform computations with the coefficients and the constants and continually rewrite the variables. We can streamline the solution process by omitting the variables until a solution is found. For example, the system

$$\begin{array}{ccccc}2x& -& 3y& =& 7,\\ \hfill x& +& 4y& =& -2\end{array}$$

can be written more simply as

$$\left[\begin{array}{cc}2& -3\\ 1& \hfill 4\end{array}|\begin{array}{c}\hfill 7\\ -2\end{array}\right].$$

The vertical line replaces the equals signs.

A rectangular array of numbers like the one above is called a matrix (pl., matrices). The matrix above is called an augmented matrix for the given system ...