rref

Type:

Command

Description:

Reduces a matrix to row-reduced echelon form, and provides a list of pivot points.

Access:

PSOLVE, Matrices, LINEAR SYSTEMS

Input:

A matrix.

Output:

Level 2/Item 1: The pivot points.

 

Level 1/Item 2: An equivalent matrix in row reduced echelon form.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear)

 

If flag –126 is clear (the default), row reduction is done with the last column. If the flag is set, row

 

reduction is done without reducing the last column, but the last column will be modified by the

 

reduction of the rest of the matrix.

Example:

Reduce to row-reduced echelon form, and find the pivot points, for the matrix:

 

 

2

1

 

Command:

 

 

3 4

 

 

rref([[2,1][3,4]])

Result:

{Pivots: {5,1.,2,1.},[[10,0][0,5]]}

See also:

RREFMOD

RREF

 

 

 

 

 

 

Type:

Command

Description:

Reduces a matrix to row-reduced echelon form. The reduction is carried out completely, so a

 

square matrix is reduced to an identity matrix. Step-by-step mode can be used to show how the

 

reduction proceeds.

Access:

Matrices, LINEAR SYSTEMS, MATRX FACTR

Input:

A matrix.

Output:

An equivalent matrix in row reduced echelon form.

Flags:

Exact mode must be set (flag –105 clear).

 

Numeric mode must not be set (flag –3 clear).

 

Step-by-step mode can be set (flag –100 set).

Example:

Solve the system of linear equations:

 

3x + 4y = 5

 

5x + 6y = 7

 

by reducing the augmented matrix that represents this system.

Command:

RREF([[3, 4, 5] [ 5, 6, 7]])

Result:

[[1, 0, -1] [0, 1, 2]]

 

This reduced matrix represents the system:

 

1x + 0y = –1

 

0x + 1y = 2

 

so that the solution is x = –1, y = 2 .

See also:

rref, RREFMOD

3-210 Full Command and Function Reference