Type: | Command |
Description: | Reduces a matrix to |
Access: | PSOLVE, Matrices, !Ø 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 |
| Numeric mode must not be set (flag |
| If flag |
| 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 |
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| 2 | 1 |
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Command: |
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| 3 4 |
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rref([[2,1][3,4]]) | ||||||
Result: | {Pivots: {5,1.,2,1.},[[10,0][0,5]]} | |||||
See also: | RREFMOD | |||||
RREF |
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Type: | Command | |||||
Description: | Reduces a matrix to | |||||
| square matrix is reduced to an identity matrix. | |||||
| reduction proceeds. | |||||
Access: | Matrices, !ØLINEAR SYSTEMS, !´MATRX FACTR | |||||
Input: | A matrix. | |||||
Output: | An equivalent matrix in row reduced echelon form. | |||||
Flags: | Exact mode must be set (flag | |||||
| Numeric mode must not be set (flag | |||||
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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, | |||||
| This reduced matrix represents the system: | |||||
| 1x + 0y = | |||||
| 0x + 1y = 2 | |||||
| so that the solution is x = | |||||
See also: | rref, RREFMOD |