Matrix Kernel

## Description

We can use Sage to find the null space of a matrix, or in other words the set of all vectors $\vec{v}$ such that $A\vec{v} = \vec{0}$

## Sage Cell

#### Code

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

## Options

#### Computing the Left Kernel

You might notice that the command we used above was `.right_kernel()`. There is also a `.left_kernel()` command, which gives us all vectors $\vec{v}$ such that $\vec{v}A = \vec{0}$

#### Code

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

#### Testing for Finiteness

We can use the `.is_finite()` method to see if a given null space is a finite set.

#### Code

```
A = matrix([[1, 2, 3], [4, 5, 6]])
nsp = A.right_kernel()
nsp.is_finite()
```

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Date: 23 Feb 2020 23:58

Submitted by: Zane Corbiere