Prentice Hall's Online Lesson Quiz Enter Web Code: aga–0407
We have seen many methods for solving a system of equations, including graphing, substitution, elimination, and Cramer's rule. Matrices can also be used to solve systems of equations. This lesson shows how to solve a system by using inverses of matrices.
In practical terms, most of these methods would not be used in the "real world" of business and industry. The method of choice will come in Section 7, that method being augmented matrices. We show this inverse method as simply one more possible choice.
Given the system of equations below, write this system with matrices by using the left and right sides of the equations. You will write a coefficient matrix, a variable matrix, and a constant matrix.
example:
Writing the system in the form of a coefficient matrix, a variable matrix, and a constant matrix appears below:
Find the inverse of the coefficient matrix.
Multiply each side of the matrix equation by the inverse matrix.
The solution is (3, 0).
Note:
To solve a system of equations with three variables, you would need to use a 3 × 3 inverse matrix, which would be very tedious. Graphing calculators and computer programs offer faster more accurate methods for these calculations. We will explore these systems using a TI-graphing calculator in class.
