Fundamental Subspace of a Matrix
Let . The nullspace (also called kernel) of is the subset of defined by
- the nullspace of A is simply the solution space of the homogeneous system of equations and is hence a subspace of
"Find a basis for Null(A)"
Given the matrix in RREF form . The solution to the homogeneous system is So we have that is a basis for Null(A) and dim(Null(A)) = 2.
Let . The column space of is the subset of defined by
Find a basis for Col(A)
To find a basis. to complete: page 167 of notes
The row space of is the subset of defined by
Note System-Rank Theorem