sentences:  Because the column space is the image of the corresponding matrix transformation, the rank of a matrix is the same as the dimension of the image.For example, the transformation R4 → R4 described by the matrix above maps all of R4 to some three-dimensional subspace.The nullity of a matrix is the dimension of the null space, and is equal to the number of columns in the reduced row echelon form that do not have pivots.