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To solve a system of linear equations, we can use substitution, elimination or something we call augmented matrices. To use matrices to solve a system of linear equations, we first enter the values associated with each of the variables and the answer. Once we put the information into a matrix (a rectangular array of numbers), we can use matrix operations to solve the equation.

### Example of an Augmented Matrix

Video Courtesy of Mr. Green of Nutshell math.

### Definitions:

**Elements**: Each of the entries in the augmented matrix**Rows**: The numbers or variables that run across the matrix.**Columns:**The numbers or variables that run down the matrix.**The diagonal of the matrix:**The set of elements that starts at the top, left corner and runs diagonally down and to the right. (This diagonal: 2, -1 and 4.)

### Citation styles

- APA style
- What Is An Augmented Matrix?. (2013, March 2). In
*ClassBrain Math Tutorials*. Retrieved 05:42, May 30, 2017, from http://www.classbrainmath.com/augmented-matrix/ - MLA style
- Cynthia Kirkeby, “What Is An Augmented Matrix?.”
*ClassBrain Math Tutorials*. 2 March 2013, 10:24 UTC. . 30 May 2017 <http://www.classbrainmath.com/augmented-matrix/>. - MHRA style
- Cynthia Kirkeby, 'What Is An Augmented Matrix?',
*ClassBrain Math Tutorials*, 2 March 2013, 10:24 UTC, <http://www.classbrainmath.com/augmented-matrix/> [accessed 30 May 2017] - The Chicago Manual of Style
- Cynthia Kirkeby, “What Is An Augmented Matrix?.”
*ClassBrain Math Tutorials*, http://www.classbrainmath.com/augmented-matrix/ [accessed May 30, 2017]. - CBE/CSE style
- Cynthia Kirkeby, What Is An Augmented Matrix? [Internet]. ClassBrain Math Tutorials; 2013 March 2, 10:24 UTC [cited 2017 May 30]. Available from: http://www.classbrainmath.com/augmented-matrix/.
- Bluebook style
- What Is An Augmented Matrix?, http://www.classbrainmath.com/augmented-matrix/ (last visited May. 30, 2017).
- AMA style
- Cynthia Kirkeby, What Is An Augmented Matrix?. ClassBrain Math Tutorials. March 2, 2013, 10:24 UTC. Available at: http://www.classbrainmath.com/augmented-matrix/. Accessed May 30, 2017.