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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