Matrices and matrix representations of linear systems
Solving systems of more than two equations in more than two variables is very cumbersome under the algebraic notation we used previously for the small notations, so we need an alternate notation. We will take the coefficients of a system of n linear equations with n unknowns denoted aij above and arrange them in a special sort of array called a matrix. What makes matrices distinct from arrays you may be accustomed to using in code is that matrices have a special multiplication operation that simplifies many calculations and, especially, makes solving larger linear systems much easier.
We will also represent the xj and the bi terms as matrices to make a single matrix equation instead of n separate equations. Once we do that, we will be ready to solve these larger systems efficiently by hand and then with Python.
Definition – Matrices and vectors
An m-by-n matrix A is a rectangular array of numbers with m rows and...