In mathematics a matrix can be categorised by its null, column and to a lesser extent its column space. These are all vector spaces associated with a particular matrix.
Null space
The null space of a 
matrix 
is as,
.
The null space is all so known as the solution space.
Column space
The column space is the vector space formed by the span of the columns of the matrix .
Row Space
The rows space is the vector space formed by the span of the rows of the matrix .