When do you need to find the Inverse in order to solve a system of equations?

Question

In class we learned how to solve a system of equations by using a matrix and performing the gauss-jordan elimination method. We also learned a method where you use the gauss-jordan method to find the inverse, and then multiply this by the matrix of the constants. In what scenario would you use each of these methods? Why would you use one over the other?

Answer 1

Suppose you have AX=b. You can reduce (A | b) and you have the answer.

Now to use inverses you need to reduce (A | I) to get A^-1. Then you need to compute A^-1 b to get X.

Now you tell me when it is best to find the inverse. I hope that you say never!