# Python sympy | Matrix.nullspace() method

• Last Updated : 13 Aug, 2019

With the help of sympy.Matrix().nullspace() method, we can find the Nullspace of a Matrix. Matrix().nullspace() returns a list of column vectors that span the nullspace of the matrix.

Syntax: Matrix().nullspace()

Returns: Returns a list of column vectors that span the nullspace of the matrix.

Example #1:

 `# import sympy ``from` `sympy ``import` `*` ` ` `M ``=` `Matrix([[``1``, ``0``, ``1``, ``3``], [``2``, ``3``, ``4``, ``7``], [``-``1``, ``-``3``, ``-``3``, ``-``4``]])``print``(``"Matrix : {} "``.``format``(M))``  ` `# Use sympy.nullspace() method ``M_nullspace ``=` `M.nullspace()  ``     ` `print``(``"Nullspace of a matrix : {}"``.``format``(M_nullspace))  `

Output:

```Matrix : Matrix([[1, 0, 1, 3], [2, 3, 4, 7], [-1, -3, -3, -4]])
Nullspace of a matrix : [Matrix([
[  -1],
[-2/3],
[   1],
[   0]]), Matrix([
[  -3],
[-1/3],
[   0],
[   1]])]
```

Example #2:

 `# import sympy ``from` `sympy ``import` `*` ` ` `M ``=` `Matrix([[``14``, ``0``, ``11``, ``3``], [``22``, ``23``, ``4``, ``7``], [``-``12``, ``-``34``, ``-``3``, ``-``4``]])``print``(``"Matrix : {} "``.``format``(M))``  ` `# Use sympy.nullspace() method ``M_nullspace ``=` `M.nullspace()  ``     ` `print``(``"Nullspace of a matrix : {}"``.``format``(M_nullspace)) `

Output:

```Matrix : Matrix([[14, 0, 11, 3], [22, 23, 4, 7], [-12, -34, -3, -4]])
Nullspace of a matrix : [Matrix([
[-1405/4254],
[   -10/709],
[  314/2127],
[         1]])]
```

My Personal Notes arrow_drop_up