# Null space

0/3
##### Intros
###### Lessons
1. Null Space Overview:
2. Definition of the Null space
$N(A) =$ null space
• A set of all vectors which satisfy the solution $Ax=0$
3. A vector u in the null space
• Multiply matrix $A$ and vector $u$
$Au=0$ means $u$ is in the null space
4. Finding a basis for the null space
• Solve for $Ax=0$
• Write the general solution in parametric vector form
• The vectors you see in parametric vector form are the basis of $N(A)$.
0/5
##### Examples
###### Lessons
1. Showing that the null space of $A$ is a subspace
Show that $N(A)$ (null space of $A$) is a subspace by verifying the 3 properties:
1) The zero vector is in $N(A)$
2) For each $u$ and $v$ in the set $N(A)$, the sum of $u+v$ is in $N(A)$ (closed under addition)
3) For each $u$ in the set $N(A)$, the vector $cu$ is in $N(A)$. (closed under scalar multiplication)
1. Verifying a vector is in the null space
Is the vector in the null space of the matrix
1. Is the vector in the null space of the matrix
1. Finding a basis for the null space
Find a basis for the null space of $A$ if:
1. Find a basis for the null space of $A$ if: