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By Kardi Teknomo, PhD.
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A linear system  can be thought as a linear transformation of a vector  in  dimensional space into vector  in  dimensional space. The solution space  of a non-homogeneous system of equations  is called the range of matrix  and the dimension of the range of matrix  is called the rank of  symbolizes as .
The dimension of the range and the null space of a matrix are related through fundamental relationship . Where  is the number of original unknowns.
See also: rank through RREF, matrix rank, matrix nullity and null space, solving system linear equations
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Preferable reference for this tutorial is
Teknomo, Kardi (2011) Linear Algebra tutorial. http:\\people.revoledu.com\kardi\
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