Linear Algebra

What is Linear Algebra?

Linear algebra is the study of linear sets of equations and their transformation properties. It allows the analysis of rotations in space,least squares fitting, solution of coupled differential equations, determination of a circle passing through three given points, as well as many other problems in mathematics, physics, and engineering. 

It is also used in vector spaces and linear mappings between such spaces. It is also the study of lines, planes, and subspaces and their intersections using algebra. Linear algebra assigns vectors as the coordinates of points in a space, so that operations on the vectors define operations on the points in the space

Why should everyone study it?

Linear algebra is said to be vital in multiple areas of science. Practically every area of modern science contains models where equations are approximated by linear equations and solving for the system helps the theory develop. It is also vital in Engineering, because it allows you to manipulate and understand whole systems of equations with huge numbers of dimensions/variables on paper without any fuss, and solve them computationally.

History of Linear Algebra
The study of linear algebra first emerged from the study of determinants, which were used to solve systems of linear equations. They were used by Leibniz in 1693, while Gabriel Cramer devised Cramer's Rule for solving linear systems in 1750. Later, Gauss further developed the theory of solving linear systems by using Gaussian elimination.