Linear independence, Nullity, etc... are the first "hints" of important mathematical questions. The one I will highlight here is "eigenmode" and "eigenvalue", in an attempt to show you why they will unfold into something important. If a physical system of interest can be represented, even approximately, by linear algebra representations, then its "natural modes" will appear out of those concepts you are learning now. What do I mean by "natural modes", here are a few examples, the vibration frequencies of a violin string (the "sound" of a violin) same for a drum

*the resonant frequencies of a bridge *the energy levels of atoms *the microwave energy distribution in a microwave oven *You will also find hints of it in any systems that use resonance, such as NMR and MRI, more at this place

I suspect (but haven't seen the math) that Google search algorithms and Netflix recommendation systems are heavy on eigenvalue/eigenvector problems too...

So, it is really important. Understanding what is "concealed" on those matrices from linear algebra that tells us about the physics of the system they described is really what you are learning now. And how to "reveal" that "concealed" information....of course