Here I have taken an example and finally figured out and
hopefully simplified the concept of the four subspaces of a Matrix
1) Column Space
2)Row Space
3)Null Space
4)Left Null Space or - Null of A - Transpose
If you start at A and look at the the Big Numbers: 1,1a,1b,2,3,4,4a
it explains what is occurring - Although you will need to know some basic Linear Algebra theory
for example ( rref.) That is just Matrix A - The rows are added together or subtracted as well as multiplied if need be
to try to obtain as many pivot Columns as possible. The outcome of those operations will determine you spaces and their relationship. Every matrix is different for the most part, ...
