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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 15:29, March 25, 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. . 25 Mar 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 25 March 2017]
The Chicago Manual of Style
Cynthia Kirkeby, “What Is An Augmented Matrix?.” ClassBrain Math Tutorials, http://www.classbrainmath.com/augmented-matrix/ [accessed March 25, 2017].
CBE/CSE style
Cynthia Kirkeby, What Is An Augmented Matrix? [Internet]. ClassBrain Math Tutorials; 2013 March 2, 10:24 UTC [cited 2017 Mar 25]. Available from: http://www.classbrainmath.com/augmented-matrix/.
Bluebook style
What Is An Augmented Matrix?, http://www.classbrainmath.com/augmented-matrix/ (last visited Mar. 25, 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 March 25, 2017.