Pivot Columns

## Description

With the `.pivots()` method, we can find the pivot columns of a matrix without needing to row reduce it. Note that Sage numbers columns starting from 0: the first column is column 0, the second is column 1, and so on.

## Sage Cell

#### Code

```
A = matrix(QQ, [[1, 2, 3], [4, 5, 6]])
A.pivots()
```

## Options

none

## Tags

CC:

Primary Tags: Linear algebra: Matrices.

Secondary Tags: Matrices: Row operations, Echelon form.

## Related Cells

- Matrices in Sage. Matrices in Sage.
- Elementary Row Operations on Matrices Using Sage to perform elementary row operations.
- Augmented Matrices. Augmenting a matrix with a column vector.
- The RREF of a matrix. Computing the RREF of a matrix.
- Finding the Free Columns of a Matrix. Finding the free columns of a matrix.

## Attribute

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Author: R. Beezer

Date: 24 Feb 2020 15:42

Submitted by: Zane Corbiere