In what field?

Every branch of science and engineering. e.g. optimizing distribution networks, predicting the weather, designing structures that won’t fall down, setting the orbits of rockets, controlling robots, simulating materials for 3d animation, designing new pharmaceutical molecules, analyzing data from high-energy physics experiments, ...

If you look at how people solve differential equations in practice, it’s all matrix algebra.

Linear algebra is also pervasive throughout pure mathematics.

Edit: I think everyone should also learn calculus though, and differential equations are the heart of calculus. Here’s an introductory calculus book http://www.math.smith.edu/~callahan/intromine.html and here’s an introductory linear algebra book https://web.stanford.edu/~boyd/vmls/ which try to get students closer to the way these tools get used in practice.