Basic and free variables
In a solution to a system of linear equations,
- Free variables (also free parameters) refer to the variables that are undetermined and may take any value. In row echelon form they correspond to a column that does not contain a leading entry.
- Basic variables (also leading variables) refer to the variables that are determined as combinations of free variables and constants. These correspond to columns that contain a leading entry.
Note that the selection of which variables are basic and which are free is arbitrary,
depending only on how the solution is written.
For example,
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