# echelon

From matlib v0.9.2
by Michael Friendly

##### Echelon Form of a Matrix

Returns the (reduced) row-echelon form of the matrix `A`

, using `gaussianElimination`

.

##### Usage

`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`

.

##### Examples

```
# NOT RUN {
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))
# }
```

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

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