Solving Matrix Equations with Inverses
Multiplicative inverses are useful for solving simple algebraic equations. For instance, the equation 2x = 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?