# gaussianElimination

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##### 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.

##### Aliases
• gaussianElimination
• print.enhancedMatrix
##### 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)

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