Indeterminate System - Conditions Giving Rise To Indeterminacy

Conditions Giving Rise To Indeterminacy

In linear systems, indeterminacy occurs if and only if the number of independent equations (the rank of the augmented matrix of the system) is less than the number of unknowns and is the same as the rank of the coefficient matrix. For if there are at least as many independent equations as unknowns that will eliminate any stretches of overlap of the equations' surfaces in the geometric space of the unknowns (aside from possibly a single point); and if the rank of the augmented matrix exceeds (necessarily by one if at all) the rank of the coefficient matrix then the equations jointly contradict each other.

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