# 2: Systems of Linear Equations

- Page ID
- 1724

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- 2.1: Gaussian Elimination
- Systems of linear equations can be written as matrix equations. Now you will learn an efficient algorithm for (maximally) simplifying a system of linear equations (or a matrix equation) -- Gaussian elimination.

- 2.3: Elementary Row Operations
- What can we do to maximally simplify a system of equations in general? We need to perform operations that simplify our system without changing its solutions. Because, exchanging the order of equations, multiplying one equation by a non-zero constant or adding equations does not change the system's solutions, we are lead to three elementary row operations:

*Thumbnail: 3 planes intersect at a point. Image used with permission (CC BY-SA 4.0; Fred the Oyster).*

## Contributor

David Cherney, Tom Denton, and Andrew Waldron (UC Davis)