Why is Linear Algebra Fascinating?

From the "719: Computational Mathematics and Fluid Dynamics", in which Margot Gerritsen and @JonKrohnLearns discuss the fundamentals of computational mathematics and its application in studying fluid dynamics. Margot also talks about how her synesthesia led to a lifelong interest in math, using computational mathematics to predict airflow, and why it is so important that underrepresented groups in data science become more visible through organizations like Women in Data Science.

[raymondfinton]

When I took linear algebra in college I struggled to understand how any of it could be applied in the real world. I felt like I was just doing arbitrary computations to get meaningless results. I wish I could see the world in the way that a pure mathematician does.