# echelon: Echelon Form of a Matrix In matlib: Matrix Functions for Teaching and Learning Linear Algebra and Multivariate Statistics

## Description

Returns the (reduced) row-echelon form of the matrix `A`, using `gaussianElimination`.

## Usage

 `1` ```echelon(A, B, reduced = TRUE, ...) ```

## 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`. `reduced` logical; should reduced row echelon form be returned? If `FALSE` a non-reduced row echelon form will be returned `...` other arguments passed to `gaussianElimination`

## Details

When the matrix `A` is square and non-singular, the reduced row-echelon result will be the identity matrix, while the row-echelon from will be an upper triagle matrix. Otherwise, the result will have some all-zero rows, and the rank of the matrix is the number of not all-zero rows.

## Value

the reduced echelon form of `X`.

John Fox

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22``` ```A <- matrix(c(2, 1, -1, -3, -1, 2, -2, 1, 2), 3, 3, byrow=TRUE) b <- c(8, -11, -3) echelon(A, b, verbose=TRUE, fractions=TRUE) # reduced row-echelon form echelon(A, b, reduced=FALSE, verbose=TRUE, fractions=TRUE) # row-echelon form A <- matrix(c(1,2,3,4,5,6,7,8,10), 3, 3) # a nonsingular matrix A echelon(A, reduced=FALSE) # the row-echelon form of A echelon(A) # the reduced row-echelon form of A b <- 1:3 echelon(A, b) # solving the matrix equation Ax = b echelon(A, diag(3)) # inverting A B <- matrix(1:9, 3, 3) # a singular matrix B echelon(B) echelon(B, reduced=FALSE) echelon(B, b) echelon(B, diag(3)) ```

matlib documentation built on April 4, 2018, 5:03 p.m.