# gaussianElimination

##### Gaussian Elimination

`gaussianElimination`

demonstrates the algorithm of row reduction used for solving
systems of linear equations of the form \(A x = B\). Optional arguments `verbose`

and `fractions`

may be used to see how the algorithm works.

##### Usage

```
gaussianElimination(A, B, tol = sqrt(.Machine$double.eps),
verbose = FALSE, latex = FALSE, fractions = FALSE)
```# S3 method for enhancedMatrix
print(x, ...)

##### Arguments

- A
coefficient matrix

- B
right-hand side vector or matrix. If

`B`

is a matrix, the result gives solutions for each column as the right-hand side of the equations with coefficients in`A`

.- tol
tolerance for checking for 0 pivot

- verbose
logical; if

`TRUE`

, print intermediate steps- latex
logical; if

`TRUE`

, and verbose is`TRUE`

, print intermediate steps using LaTeX equation outputs rather than R output- fractions
logical; if

`TRUE`

, try to express non-integers as rational numbers- x
matrix to print

- ...
arguments to pass down

##### Value

If `B`

is absent, returns the reduced row-echelon form of `A`

.
If `B`

is present, returns the reduced row-echelon form of `A`

, with the
same operations applied to `B`

.

##### Examples

```
# NOT RUN {
A <- matrix(c(2, 1, -1,
-3, -1, 2,
-2, 1, 2), 3, 3, byrow=TRUE)
b <- c(8, -11, -3)
gaussianElimination(A, b)
gaussianElimination(A, b, verbose=TRUE, fractions=TRUE)
gaussianElimination(A, b, verbose=TRUE, fractions=TRUE, latex=TRUE)
# determine whether matrix is solvable
gaussianElimination(A, numeric(3))
# find inverse matrix by elimination: A = I -> A^-1 A = A^-1 I -> I = A^-1
gaussianElimination(A, diag(3))
inv(A)
# }
```

*Documentation reproduced from package matlib, version 0.9.2, License: GPL (>= 2)*