Last updated April 10, 2022

Status: Tags: #cards/math232/unit3 Links: Linear Mapping

Nullspace

Principles

Nullspace ?

• Set of all vectors whose image under L is the zero vector
• Nullspace is subspace
• Solution space of homogeneous equation

As a linear mapping ?

Prove that nullspace is a subspace ?

Dimension of nullspace is ?

• number of free variables
• num columns - rank

• Four fundamental subspaces

Examples

• Find nullspace of ?
• Create matrix, row reduce, back substitution to find solution set of vectors (x1,x2,x3) where L(x) = 0
• 
• is basis for Null(L)

Check if vector x is in nullspace A ?

• If Ax = 0, it is in nullspace
• If it is in the nullspace, then Ax = 0

Backlinks

1

list from Nullspace AND !outgoing(Nullspace)

References:

Created:: 2022-02-01 15:44