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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

 Ax=b
(1)

by forming the column-appended augmented matrix

 (A|b).
(2)

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

 (A|I)
(3)

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

 (I|A^(-1)).
(4)

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

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References

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. https://mathworld.wolfram.com/AugmentedMatrix.html

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