Overdetermined system

#1 A system of three linearly independent equations, three lines, three intersections

#2 A system of three linearly independent equations, three lines (two parallel), two intersections

#3 A system of three linearly independent equations, three lines (three parallel), no intersections

#4 A system of three equations (one equation linearly dependent on the others), three lines (two collinear), one intersection

In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.

单词	Overdetermined system
释义	Overdetermined system 英语百科 Overdetermined system In mathematics, a system of equations is considered overdetermined if there are more equations than unknowns. An overdetermined system is almost always inconsistent (it has no solution) when constructed with random coefficients. However, an overdetermined system will have solutions in some cases, for example if some equation occurs several times in the system, or if some equations are linear combinations of the others.
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