I am going into Computer engineering and I have heard that there is a lot of Linear Algebra in it. Exactly how and why do they use so much linear algebra?
Solving systems of linear equations (which may appear in (say) multiloop circuits) uses linear algebra.
Graph theory and networks (which may arise in discussions of parallel computing) use incidence and adjacency matrices, which are studied with linear algebra.
FFT and other signal processing methods use linear algebra.