Linear algebra wasn't built in a day. It took nearly 200 years of ideas, from Leibniz's determinants in 1693 to Peano's formal definition of vector spaces in 1888.
Along the way, Cramer found a way to solve linear systems, Gauss developed elimination methods, and Sylvester gave matrices their name.
One equation captures much of this journey: Ax = b. Behind those three symbols lies a mathematical language that now powers computer graphics, engineering, AI and modern physics.