### 1. Goal

The goal of linear algebra is to solve systems of linear equations, and tell if the solution is unique or not. Besides, linear algebra aims to transform spaces.

### Objects

In elementary algebra operations are performed on numbers, e.g.:

As we’ll see, in linear algebra operations are performed on matrices and vectors, e.g. :

### Recapitulation

In linear algebra operations are no longer performed on numbers but on matrices and vectors. These one are a generalization of the concept of number.

Indeed, in $(2)$, the vector $\vec{x}$ has two entries. We can see numbers as vectors but having one single element.