Spaces of vectors associated with a matrix

Here are a few examples of how you can use Maple to find the reduced row exhelon form of a matrix and to obtain bases in the Row space, Column space and Nullspace of a matrix.

>	with(LinearAlgebra);

>	A:=Matrix([[1,4,5,6,9],[3,-2,1,4,-1],[-1,0,-1,-2,-1],[2,3,5,7,8]]);

>	ReducedRowEchelonForm(A);

>	NullSpace(A);

>	RowSpace(A);

>	ColumnSpace(A);

You can also find the rank of the matrix, which is nothing but the common dimension of the row and column spaces of A.

>

Rank(A);

>