# How do I solve a system of equations using inverse matrices?

##### 1 Answer

Consider a normal equation in

To solve this equation you simply take the

at this point you can "read" the solution as:

With a system of **inverse matrix** in place of the coefficient to the -1 (in our example is

You can use matrices and change your system in a **matrix equation** :

If you have the following system:

(where

you can change it in a matrix equation:

Where

*You can check that this representation with matrices represents the system by doing the multiplication #A*U# and setting it equal to #B# you'll get back your original system!!!*

Now, to solve your matrix equation

(Remembering that **identity matrix** .

For example:

So: