---
kind: statement
msc:
- 15A06
name: Inconsistency of a linear system and a pivot in the last column
role: proposition
sources:
- locator: src/section1-4.xml:575
  url: https://github.com/davidaustinm/ula/blob/b6ea263ef23703072b7007485bb7a2d89c5f399b/src/section1-4.xml#L575
tag: BKA191KD1S
uses:
- 0GT4WWGWH2
- 0T6MWGZSXA
- 0J0BBCMJ5W
- 0X6V9B1V10
---

## Statement

Take a [[linear system|0GT4WWGWH2]] and form its [[augmented matrix|0T6MWGZSXA]].
The system is [[inconsistent|0X6V9B1V10]] exactly when the rightmost column of that matrix holds a [[pivot|0J0BBCMJ5W]] position.
So the system has at least one solution exactly when the rightmost column has no pivot position.