When Gauss-Jordan elimination transforms a matrix representing an inconsistent system of linear equations to reduced row-echelon form, a matrix row containing all zero coefficient entries and a non-zero constant entry is produced, indicating that the system has no solutions. This lecture shows how inconsistent systems can sometimes be spotted by simply looking at the equations. Examples of three-variable systems represented by groups of planes are then used to show how certain configurations of planes can cause inconsistency, and why this leads to the indication of inconsistency produced during Gauss-Jordan elimination.
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