Math 2.0

Linear and multilinear algebra; matrix theory Proposition

Inconsistency of a linear system and a pivot in the last column

Builds on System of linear equationsAugmented matrixPivotConsistent and inconsistent systems

Statement

Take a linear system and form its augmented matrix. The system is inconsistent exactly when the rightmost column of that matrix holds a pivot position. So the system has at least one solution exactly when the rightmost column has no pivot position.

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Augmented matrix, concept, no evidence levelAugmented matrixconceptConsistent and inconsistent systems, concept, no evidence levelConsistent and incons…conceptPivot, concept, no evidence levelPivotconceptSystem of linear equations, concept, no evidence levelSystem of linear equa…conceptInconsistency of a linear system and a pivot in the last column, statement, no evidence levelInconsistency of a li…statement
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Augmented matrix concept
  2. Consistent and inconsistent systems concept
  3. Pivot concept
  4. System of linear equations concept
  5. Inconsistency of a linear system and a pivot in the last column statement

Further reading

  1. Web https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section1-4.xml#L575, src/section1-4.xml:575
About this page
TagBKA191KD1S
URIm2://BKA191KD1S
Kindstatement, proposition
WritingW0 stub
MSC15A06
StatusThis copy of the site has no build data. Run m2 status BKA191KD1S.
UsesSystem of linear equations, Augmented matrix, Pivot, Consistent and inconsistent systems
Changed4 November 2026

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