# Pivot columns in a Matrix

flyingpig

## Homework Statement

Just need help identifying pivots columns

$$\begin{bmatrix} 1 & 1 & 1 &1 &1\\ 0& 0& 0& 0&0\\ 0& 0& 0& 0&9 \end{bmatrix}$$

From my understanding, any column with 1s and everything below it 0s are all pivot columns right?

Is the above all pivot columns? Also for a 3 x 5 coefficent matrix that has three pivot columns, is the system consistent?

The book says it is not, but why? The one above is a counterargument given by me. Does anyone know the LaTeX code to make an augmented matrix? Like put a bar before the constants

flyingpig
The last column number should be a 0 not 9

Whitishcube
remember, the definition of a pivot column is essentially that the column contains a pivot position in reduced echelon form. a pivot is the first nonzero term in the row (which needs to be a 1 for it to be reduced echelon form). how many of your rows in that matrix have a pivot in them?

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flyingpig
There can only be one pivot column in every row?

Whitishcube
There can only be one pivot position in each row. Notice that there is a subtle difference between a pivot column and a pivot itself.