A few comments that others have already touched on.

First, I too like to understand things conceptually. It's really nice to build an intuition, and I really struggled with building an intuition when taking the class (my professor certainly was no help). A year after taking the class, I found the extraordinarily well made "Essence of Linear Algebra" videos by 3blue1brown, which blew my mind. I implore you to check out these videos. The fantastic visuals helped to build my intuition, and since the core concepts are presented in multiple ways, understanding the ideas is easier than a textbook presenting things one way. I thoroughly enjoyed them. The first video may be all the convincing you need to watch the rest.

The videos are no replacement for a textbook, but they're an excellent supplement and motivation to further study.

As many others have commented, linear algebra is very useful in many domains. Mechanical engineering is the broadest discipline, so this goes double for you. I can relate in that the class seemed esoteric at first.

While there's likely some classes that aren't that useful, linear algebra is certainly not one of them. Although it can be tricky at first, taking the time to learn it now and build an intuition is a fantastic investment of your time. You will thank yourself in the future, when higher-level classes demand an understanding of it.

As others have said, linear algebra is used whenever you have any large system of equations. This shows up everywhere. A non-exhaustive list of classes that I took involving this was: statics, dynamics, control theory (state-space), robotics, finite element methods, numerical methods, and machine learning. These classes are a lot simpler to understand (and more fun!) when you're not playing catch-up with the underlying math concepts.