Column Space

## Description

We can use Sage to find the column space of a given matrix. The Sage cell below computes the column space of

(1)\begin{align} A = \begin{pmatrix} 2 & 3 & 5 \\ 7 & 11 & 13 \\ 17 & 19 & 23 \end{pmatrix} \end{align}

over the rational numbers, $\mathbb Q$.

## Sage Cell

#### Code

```
A = matrix(QQ, [[ 2, 3, 5],
[ 7, 11, 13],
[17, 19, 23]])
A.column_space()
```

## Options

none

## Tags

CC:

Primary Tags: Linear Algebra: Euclidean spaces

Secondary Tags: Euclidean spaces: Row, column, and null spaces

## Related Cells

- Right and Left System Solving Finding solutions to the equations $A\mathbf{x} = \mathbf{b}$ and $\mathbf{x}A = \mathbf{b}$.
- The Kernel of a Matrix Finding the kernel (or null space) of a matrix.
- Linear Combinations of Vector Building Linear Combinations in Sage.

## Attribute

Permalink:

Author: Rob Beezer

Date: 02 Apr 2020 22:11

Submitted by: Zane Corbiere