Deep understanding of the mathematics behind a given problem space can help you later in the applications. So maybe they'll never have to actually implement Gauss Jordan (and they shouldn't), but the core ideas of normalization and reduction are very important to any sort of numerical methods and come up again and again.

As a somewhat related example, our engineering college required a calculus based probability course that probably 95% of the engineers dreaded. Conditional probability, multivariable PDFs etc. A few years after college, I had the (dis)pleasure of needing to generate random values from an unknown PDF, given only the cumulative distribution. To a statistician, the obvious answer is to use the inverse CDF (a simple interpolated lookup table based on the known CDF) and a uniform random, but an engineer who didn't fully grok the probability basics would probably have just hacked around it, trying different approximations until something stuck.

Neither approach is right or wrong, but sometimes simply understanding the essential material and methods gives you unforeseen insights later on.