5.106 How to find column space of matrix?

Do not use the Maple command LinearAlgebra:-ColumnSpace for this. it gives the columns in the RREF. The correct way is to obtain the corresponding columns of the pivot columns in the original matrix \(A\). Hence use the command Basis like this

A:=Matrix([[1,0,0],[1,1,1]]); 
LinearAlgebra:-Basis([seq(A[..,i],i=1..LinearAlgebra:-ColumnDimension(A) )]);
 

Which gives

\[ \left [\left [\begin {array}{c} 1 \\ 1 \end {array}\right ], \left [\begin {array}{c} 0 \\ 1 \end {array}\right ]\right ] \]

If you use ColumnSpace command you’ll get this

A:=Matrix([[1,0,0],[1,1,1]]); 
LinearAlgebra:-ColumnSpace(A);
 

\[ \left [\left [\begin {array}{c} 1 \\ 0 \end {array}\right ], \left [\begin {array}{c} 0 \\ 1 \end {array}\right ]\right ] \]

These are different. Basis is the correct command to use, which matches the standard definition in textbooks.