It's applied pretty much everywhere. Most numerical problems have some linear algebra component to them. Physics uses it a lot too. A lot of non-linear problems

It's applied pretty much everywhere. Most numerical problems have some linear algebra component to them. Physics uses it a lot too. A lot of non-linear problems have a linearization on which you can use linear algebra to obtain approximations. Ideas from linear algebra are used a lot in things like signal processing, quantum mechanics, etc.