- Augmented matrix
In
linear algebra , the augmented matrix of a matrix is obtained by combining two matrices.Given the matrices "A" and "B", where:
Then, the augmented matrix ("A"|"B") is written as:
This is useful when solving systems of linear equations or the augmented matrix may also be used to find the inverse of a matrix by combining it with the
identity matrix .Examples
Let "C" be a square 2×2 matrix where
To find the inverse of C we create ("C"|"I") where I is the 2×2
identity matrix . We then reduce the part of ("C"|"I") corresponding to "C" to the identity matrix using onlyelementary matrix transformations on ("C"|"I").As used in linear algebra, an augmented matrix is used to represent the
coefficients and thesolution vector of each equation set.For the set of equations:the augmented matrix would be composed of
Leaving us with:
.
References
* Marvin Marcus and Henryk Minc, "A survey of matrix theory and matrix inequalities",
Dover Publications , 1992, ISBN 0-486-67102-X. Page 31.
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