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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