Chapter 4 System of Linear Equations Section 4.4 More general Systems
To conclude this module, we will briefly discuss two further details concerning systems of linear equations.
Firstly, in systems of linear equations free parameters can occur. These are variable quantities - so-called tuning parameters - which may strongly affect the behaviour of the systems, and especially the solution sets. Sometimes it is advantageous not to fix all coefficients and right-hand sides of the equations, but to keep them variable to investigate what happens for different values. Sometimes not all coefficients and right-hand sides are known from the problem description.
Secondly, in a system of linear equations either the number of linear equations or the number of variables need not be the same.