# gaussianElimination: Gaussian Elimination In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

## Description

`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

 ```1 2``` ```gaussianElimination(A, B, tol = sqrt(.Machine\$double.eps), verbose = FALSE, latex = FALSE, fractions = FALSE) ```

## 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

## 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`.

John Fox

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14``` ``` 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) ```

matlib documentation built on May 30, 2017, 1:49 a.m.