We can use Gaußian Elimination (GE) to help us solve larger systems of equations. If we have a matrix $A \in \mathbb{K}^{m \times n}$, where $\mathbb{K} \in \{ \mathbb R, \mathbb C, \mathbb G \}$, what are the potential problems with using GE?
I'm pretty sure we run into rounding errors if the values in the matrix have a large difference between them, i.e., if $a_{0,0}=0.00002$ and $a_{0,4}=120000$, but I'm not 100% sure.
Gaussian elimination is well-known to be sensitive to numerical rounding errors, especially with ill-conditioned matrices. To reduce this problem, two pivoting strategies (namely partial and total) are classical.
There is a complete theory of roundoff errors in linear algebra and in Gaussian elimination in particular. But this is not a simple topic, I have to refer you to a textbook. (E.g. Matrix Computation by G. Golub & al.)