Manuals/calci/REDUCEDROWECHELONFORM

REDUCEDROWECHELONFORM (Array)

• $Array$ is the set of values.

Description

• This function shows the value of the Row reducedchelon form.
• In $REDUCEDROWECHELONFORM(Array)$,$Array$ is the set of values.
• Reduced row echelon form is also called Row canonical form.
• A matrix that has gone under Gaussian elimination is said to be in row echelon form.
• Row echelon form satisfies the following conditions:

1. All nonzero rows precede zero rows when both types are contained in the matrix.
2. The first (leftmost) nonzero element of each nonzero row is unity (the number 1).
3. When the first nonzero element of a row appears in column , then all other elements in the same column are zero 
4. The first nonzero element of any nonzero row appears in a later column  than the first nonzero element of any preceding row.

• The following 3x5 matrix is an example of row echelon matrix:

${\begin{bmatrix}1&0&a_{1}&0&b_{1}\\0&1&a_{2}&0&b_{2}\\0&0&0&1&b_{3}\end{bmatrix}}$

Examples

1. REDUCEDROWECHELONFORM([ [ 1, 2, -1, -4], [ 2, 3, -1,-11], [-2, 0, -3, 22]])

1	0	0	-8
0	1	0	1
0	0	1	-2

2. REDUCEDROWECHELONFORM([[2,3,1,0],[10,2,6,-18]])

1	0	0.6153846153846154	-2.0769230769230766
0	1	-0.07692307692307693	1.3846153846153846

See Also

• QRDECOMPOSITION
• CHOLESKYFACTORIZATION
• CONFERENCE

References

• Row Echelon form

• List of Main Z Functions

• Z3 home