Story so far..

We began by learning how to represent linear equations by matrices as . Then we learned how these are manipulated by elementary operations so that the solutions are easy to read off.

Then we defined elementary matrices and which accomplish the desired tasks, so that matrix multiplications replace the required operations.

Therefore, we introduced the formal algebra of matrices and studied some of its properties.

One nice way of solving occurs if we can find some matrix such that . In this case, the solution is simply given as . We study later when it can be done and how the matrix can then be found.