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
(1)
|
by forming the column-appended augmented matrix
(2)
|
Augmented matrices can also be used to find a matrix inverse of by forming
(3)
|
with the identity matrix of appropriate dimension, then using elementary row operations to reduce the result to the form
(4)
|
The payoff matrix in game theory is a case of a more complicated augmented matrix .