# Python program to add two Matrices

• Difficulty Level : Medium
• Last Updated : 21 Jul, 2022

Aim : Program to compute the sum of two matrices and then print it in Python.

Examples:

```Input :
X= [[1,2,3],
[4 ,5,6],
[7 ,8,9]]

Y = [[9,8,7],
[6,5,4],
[3,2,1]]

Output :
result= [[10,10,10],
[10,10,10],
[10,10,10]]```

We can perform matrix addition in following ways in Python.

Using for loop:

Implementation:

## Python

 `# Program to add two matrices using nested loop` `X ``=` `[[``1``,``2``,``3``],``    ``[``4` `,``5``,``6``],``    ``[``7` `,``8``,``9``]]` `Y ``=` `[[``9``,``8``,``7``],``    ``[``6``,``5``,``4``],``    ``[``3``,``2``,``1``]]`  `result ``=` `[[``0``,``0``,``0``],``        ``[``0``,``0``,``0``],``        ``[``0``,``0``,``0``]]` `# iterate through rows``for` `i ``in` `range``(``len``(X)):  ``# iterate through columns``    ``for` `j ``in` `range``(``len``(X[``0``])):``        ``result[i][j] ``=` `X[i][j] ``+` `Y[i][j]` `for` `r ``in` `result:``    ``print``(r)`

Output

```[10, 10, 10]
[10, 10, 10]
[10, 10, 10]```

Time Complexity: O(len(X) * len(X)), as we are using nested loop for traversing the matrix.
Auxiliary Space: O(len(X) * len(X)), as we are using a result matrix which is extra space.

Another Approach:

1. Explanation :- In this program we have used nested for loops to iterate through each row and each column. At each point we add the corresponding elements in the two matrices and store it in the result.
2. Using nested list comprehension : In Python, we can implement a matrix as nested list (list inside a list). We can treat each element as a row of the matrix.

Implementation:

## Python

 `# Program to add two matrices``# using list comprehension`` ` `X ``=` `[[``1``,``2``,``3``],``    ``[``4` `,``5``,``6``],``    ``[``7` `,``8``,``9``]]`` ` `Y ``=` `[[``9``,``8``,``7``],``    ``[``6``,``5``,``4``],``    ``[``3``,``2``,``1``]]` `result ``=` `[[X[i][j] ``+` `Y[i][j]  ``for` `j ``in` `range``(``len``(X[``0``]))] ``for` `i ``in` `range``(``len``(X))]`` ` `for` `r ``in` `result:``    ``print``(r)`

Output

```[10, 10, 10]
[10, 10, 10]
[10, 10, 10]```

Time Complexity: O(len(X) * len(X)), as we are using nested loop for traversing the matrix.
Auxiliary Space: O(len(X) * len(X)), as we are using a result matrix which is extra space.

Another Approach:

1. Explanation:-
The output of this program is the same as above. We have used nested list comprehension to iterate through each element in the matrix. List comprehension allows us to write concise codes and we must try to use them frequently in Python. They are very helpful.
2. Using zip() and sum

Implementation:

## Python

 `# Program to add two matrices``# using zip()`` ` `X ``=` `[[``1``,``2``,``3``],``    ``[``4` `,``5``,``6``],``    ``[``7` `,``8``,``9``]]`` ` `Y ``=` `[[``9``,``8``,``7``],``    ``[``6``,``5``,``4``],``    ``[``3``,``2``,``1``]]` `result ``=` `[``map``(``sum``, ``zip``(``*``t)) ``for` `t ``in` `zip``(X, Y)]`` ` `print``(result)`

Output

`[[10, 10, 10], [10, 10, 10], [10, 10, 10]]`

Time Complexity: O(len(X) * len(X)), as we are using zip function.
Auxiliary Space: O(len(X) * len(X)), as we are using extra space.

Explanation :- The zip function accepts iterator i of each element(list) of matrix, mapping them, adding them using sum() and storing them in the map form.

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