# linear systems as matrices

(2 hours to learn)

## Summary

We can represent systems of linear equations in terms of matrices and vectors. This allows us to analyze and solve them using the tools of linear algebra.

## Context

This concept has the prerequisites:

- vectors (Linear systems are represented in terms of matrix-vector multiplication.)

## Core resources (read/watch one of the following)

## -Free-

→ MIT Open Courseware: Linear Algebra (2011)

Videos for an introductory linear algebra course focusing on numerical methods.

## -Paid-

→ Introduction to Linear Algebra

An introductory linear algebra textbook with an emphasis on numerical methods.

Location:
Section 2.1, pages 31-38

## Supplemental resources (the following are optional, but you may find them useful)

## -Free-

→ Khan Academy: Linear Algebra

## -Paid-

→ Multivariable Mathematics

A textbook on linear algebra and multivariable calculus with proofs.

Location:
Section 4.1, "Gaussian elimination and the theory of linear systems," pages 127-142

## See also

- There are many techniques for solving linear systems that involve matrix operations such as: Computing the LU factorization is a computationally efficient method for solving linear systems