Augmented Matrix

An augmented matrix is a matrix obtained by adjoining a row or column vector, or sometimes another matrix with the same vertical dimension.

The most common use of an augmented matrix is in the application of Gaussian elimination to solve a matrix equation of the form


by forming the column-appended augmented matrix


Augmented matrices can also be used to find a matrix inverse of A by forming


with I the identity matrix of appropriate dimension, then using elementary row operations to reduce the result to the form


The payoff matrix in game theory is a case of a more complicated augmented matrix .

See also

Column Vector, Gaussian Elimination, Matrix, Matrix Equation, Matrix Inverse, Payoff Matrix, Row Vector

Explore with Wolfram|Alpha


Marcus, M. and Minc, H. A Survey of Matrix Theory and Matrix Inequalities. New York: Dover, p. 31, 1992.

Cite this as:

Weisstein, Eric W. "Augmented Matrix." From MathWorld--A Wolfram Web Resource.

Subject classifications