Reduced Row Echelon Form

Example

Find the Reduced Row Echelon of the given matrix A:

A = {{2,4,6,-6,0,0,0},{3,-5,3,-3,1,0,0},{4,9,-4,4,0,-1,0},{0,1,0,0,0,0,1}};
A // MatrixForm

ReducedA = RowReduce[A];
ReducedA // MatrixForm

MatrixRank[A]

NullSpace[A]

In case that we would like to compute the Reduced Row Echelon form of the augmented matrix for Ax = b:

b = {{11},{11},{12},{4}};
b// MatrixForm

AugmentedMatrix = Join[ A,b, 2];
AugmentedMatrix // MatrixForm

RowReduce[AugmentedMatrix] // MatrixForm