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# Python sympy | Matrix.rref() method

With the help of sympy.Matrix().rref() method, we can put a matrix into reduced Row echelon form. Matrix().rref() returns a tuple of two elements. The first is the reduced row echelon form, and the second is a tuple of indices of the pivot columns.

Syntax: Matrix().rref()

Returns: Returns a tuple of which first element is of type Matrix and second one is of type tuple.

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.rref() method ``M_rref ``=` `M.rref()  ``     ` `print``(``"The Row echelon form of matrix M and the pivot columns : {}"``.``format``(M_rref))  `

Output:

```Matrix : Matrix([[1, 0, 1, 3], [2, 3, 4, 7], [-1, -3, -3, -4]])
The Row echelon form of matrix M and the pivot columns : (Matrix([
[1, 0,   1,   3],
[0, 1, 2/3, 1/3],
[0, 0,   0,   0]]), (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.rref() method ``M_rref ``=` `M.rref()  ``     ` `print``(``"The Row echelon form of matrix M and the pivot columns : {}"``.``format``(M_rref))  `

Output:

```Matrix : Matrix([[14, 0, 11, 3], [22, 23, 4, 7], [-12, -34, -3, -4]])
The Row echelon form of matrix M and the pivot columns : (Matrix([
[1, 0, 0, 1405/4254],
[0, 1, 0,    10/709],
[0, 0, 1, -314/2127]]), (0, 1, 2))
```