|Mar18-10, 06:23 AM||#1|
Unique solution of an overdetermined system
If I want to know how many solutions a consistent linear system with more equations than unknowns has, how do I tell? Obviously there is either 1 solution of infinite solutions. Can you have a free variable in this case? I'm confused how to find out whether a system will give a unique solution.
|Mar18-10, 06:49 AM||#2|
You need to determine how many independent equations there are. If the system really is consistent, then there must be no more independent equations than unknown variables. That is, if n is the number of variables and m is the number of independent equations, then [itex]n\ge m[/itex]. The number of free variables is n- m.
If you write the coefficient matrix for the system and row-reduce, the number of independent equations is the number of non-zero rows.
|Similar Threads for: Unique solution of an overdetermined system|
|system equations - unique / no / infinite solution||Linear & Abstract Algebra||2|
|Existence of a unique solution?||Calculus & Beyond Homework||1|
|Unique solution||Calculus & Beyond Homework||3|
|Diff Eq Region of Unique Solution||Calculus & Beyond Homework||2|
|IVP unique solution||Introductory Physics Homework||6|