Term
How do you find the column space of A? 

Definition
The column space of A is the set of all b for which the system has a solution 


Term
How do you create an explicit description of Nul A? 

Definition
To create an explicit description of Nul A, solve the equation Ax = 0 and write the solution in parametric vector form. 


Term
What is the standard basis for R^n? 

Definition
The set {e1,...,en} is the standard basis for R^n. 


Term
How do you find a basis for the null space of a matrix? 

Definition
If the matrix is A, solve Ax = 0 by creating an augmented matrix and row reducing. Then write your answer in parametric vector form. Once in parametric vector form, the vectors that are left (pivot columns) form basis for Nul A which is automatically linearly independent. 

