Any fields that have anything to do with video, image, audio, games, machine learning.

Just to have a taste of use cases: compression, filters(image filters for de-noising, HP & LP filters for audio), encoding/decoding, computer vision techniques, cryptography, neural nets, computer graphics (this is where most people learn how to use it in real computer programs)

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.

- scale or rotate an image.

- root finding algorithm with more than one variable.

- graph problems like Google's PageRank

- statistical analysis

- 3d rendering (projecting a 3d scene onto a 2d image)

- solving systems of equation (also see linear programming)

Linear algebra is very basic and fundamental to physics and math.