## Solving Matrix Equations with Inverses

Multiplicative inverses are useful for solving simple algebraic equations. For instance, the equation 2*x* = 6 may be solved by multiplying both sides of the equation by the multiplicative inverse of 2. When we do this, we get ^{1}⁄_{2}(2x) = ^{1}⁄_{2}(6). Since ^{1}⁄_{2}·2 = 1, the solution of the equation is *x* = 3.

In this section, we’ll learn how to write a system of linear equations as a matrix equation *AX* = *B*. This matrix equation is solved by multiplying both sides by an inverse matrix. This allows us to solve systems of equations with a strategy different from the matrix methods we used in Chapter 2.

**Read **in Section 3.4

- How do you write a system of equations as a matrix equation?
- How do you solve a matrix equation using the matrix inverse?

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