5.97 Basis for Null space, Row space and column space of matrix

Given

\[ \left [\begin {array}{cccc}1 & -1 & 0 & 2 \\1 & 2 & 2 & -2 \\0 & 2 & 3 & -1 \end {array}\right ] \]

Find its Null, Row and Column space basis vectors.

restart; 
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]); 
LinearAlgebra:-NullSpace(A)
 

\[ \left \{ \left [\begin {array}{c}0 \\2 \\-1 \\1 \end {array}\right ] \right \} \]

restart; 
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]); 
LinearAlgebra:-RowSpace(A)
 

\[ \left [\left [\begin {array}{cccc}1 & 0 & 0 & 0 \end {array}\right ], \left [\begin {array}{cccc}0 & 1 & 0 & -2 \end {array}\right ], \left [\begin {array}{cccc}0 & 0 & 1 & 1 \end {array}\right ]\right ] \]

restart; 
A:=Matrix([[1,-1,0,2],[1,2,2,-2],[0,2,3,-1]]); 
LinearAlgebra:-ColumnSpace(A)
 

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