rref
Reduced Row Echelon Form
Produces the reduced row echelon form of A
using
Gauss Jordan elimination with partial pivoting.
 Keywords
 math
Usage
rref(A)
Arguments
 A
 numeric matrix.
Details
A matrix of ``rowreduced echelon form" has the following characteristics:
1. All zero rows are at the bottom of the matrix
2. The leading entry of each nonzero row after the first occurs to the right of the leading entry of the previous row.
3. The leading entry in any nonzero row is 1.
4. All entries in the column above and below a leading 1 are zero.
Roundoff errors may cause this algorithm to compute a different value
for the rank than rank
, orth
or null
.
Value

A matrix the same size as
m
.
Note
This serves demonstration purposes only; don't use for large matrices.
References
Weisstein, Eric W. ``Echelon Form." From MathWorld  A Wolfram Web Resource. http://mathworld.wolfram.com/EchelonForm.html
See Also
Examples
A < matrix(c(1, 2, 3, 1, 3, 2, 3, 2, 1), 3, 3, byrow = TRUE)
rref(A)
# [,1] [,2] [,3]
# [1,] 1 0 0
# [2,] 0 1 0
# [3,] 0 0 1
A < matrix(data=c(1, 2, 3, 2, 5, 9, 5, 7, 8,20, 100, 200),
nrow=3, ncol=4, byrow=FALSE)
rref(A)
# 1 0 0 120
# 0 1 0 0
# 0 0 1 20
# Use rref on a rankdeficient magic square:
A = magic(4)
R = rref(A)
zapsmall(R)
# 1 0 0 1
# 0 1 0 3
# 0 0 1 3
# 0 0 0 0