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# Python PyTorch – torch.linalg.solve() Function

Example:

```Let's consider the  linear equations :
6x + 3y = 1
3x - 4y = 2
Then M values can be - [[6,3],[3,-4]]
and t is [1,2]```

## torch.linalg.solve() Function

The torch.linalg.solve() method is used to solve a square system of linear equations with a unique solution. It will take two parameters, in which the first parameter is a matrix that is a tensor and the second parameter is also a tensor with one dimension.

Syntax: torch.linalg.solve(M, t)

Parameters:

• M is an tensor matrix
• t is a tensor vector.

Return: It will return a tensor.

### Example1:

In this example, we will Solve the linear equation – 6x + 3y = 1, 3x – 4y = 2 and check the solution is true or not. Here M is [[6,3],[3,-4]] and t [1,2]. After that we will apply torch.linalg.solve() method to return unique tensor solution. Finally we will use torch.allclose() method to check  the equation is true or not.

## Python3

 `# import torch ` `import` `torch ` ` `  `''' ` `Let's consider the  linear equations : ` `6x + 3y = 1 ` `3x - 4y = 2 ` `Then M values can be - [[6,3],[3,-4]] ` `and t is [1,2] ` `'''` ` `  `# consider M which is an 2 D tensor that ` `# has 2 elements each ` `M ``=` `torch.tensor([[``6.``, ``3.``], [``3.``, ``-``4.``]]) ` ` `  `# consider t which is 1D that has two elements ` `t ``=` `torch.tensor([``1.``, ``2.``]) ` ` `  `# Solve  the equation using linalg.solve(M,t) ` `solved ``=` `torch.linalg.solve(M, t) ` ` `  `# display the solved solution ` `print``(solved) ` ` `  `# check the solution is true or not using ` `# allclose() method ` `print``(torch.allclose(M @ solved, t)) `

Output:

```tensor([ 0.3030, -0.2727])
True```

### Example 2:

In this example, we will Solve the linear equation – 6x + 3y = 1,3x – 4y = 2 and check the solution is true or not. Here the elements of M is [[6,3],[3,-4]] and t is [0,2]. After that, we will apply torch.linalg.solve() method which will return a unique tensor solution. Finally, we will use a torch.allclose() method to check whether the equation is true or not.

## Python3

 `# import torch ` `import` `torch ` ` `  `''' ` `Let's consider the  linear equations : ` `5x - 3y = 0 ` `3x - 4y = 2 ` `Then M values can be - [[5,-3],[3,-4]] ` `and t is [0,2] ` `'''` ` `  `# consider M which is an 2 D tensor that  ` `# has 2 elements each ` `M ``=` `torch.tensor([[``5.``, ``-``3.``], [``3.``, ``-``4.``]]) ` ` `  `# consider t which is an 1 D tensor that ` `# has 2 elements ` `t ``=` `torch.tensor([``0.``, ``2.``]) ` ` `  `# Solve the equation using linalg.solve(M,t) ` `# method ` `solved ``=` `torch.linalg.solve(M, t) ` ` `  `# display the solved solution ` `print``(solved) ` ` `  `# check the solution is true or not using ` `# allclose() method ` `print``(torch.allclose(M @ solved, t)) `

Output:

```tensor([-0.5455, -0.9091])
True```

### Example 3:

In this example, we will Solve the linear equation –  9x – y = 0, 3x – 4y = 0 and check the solution is true or not. Here the elements of M is [[9,-1],[3,-4]] and t [0,0]. After that, we will apply the torch.linalg.solve() method which will return a unique tensor solution, and last we will use a torch.allclose() method to check whether the equation is true or not.

## Python3

 `# import torch ` `import` `torch ` ` `  `''' ` `Solve the linear equation - 9x - y = 0, ` `3x - 4y = 0 and check the solution is true or not ` ` `  `Here the elements of M is - [[9,-1],[3,-4]] and t - [0,0]. ` `'''` ` `  `# consider M which is an 2 D tensor that  ` `# has 2 elements each ` `M ``=` `torch.tensor([[``9.``, ``-``1.``], [``3.``, ``-``4.``]]) ` ` `  `# consider t which is an 1 D tensor that  ` `# has 2 elements ` `t ``=` `torch.tensor([``0.``, ``0.``]) ` ` `  `# Solve t using linalg.solve(M,t) method ` `solved ``=` `torch.linalg.solve(M, t) ` ` `  `# display the solved solution ` `print``(solved) ` ` `  `# check the solution is true or not using  ` `# allclose() method ` `print``(torch.allclose(M @ solved, t)) `

Output:

```tensor([0., -0.])
True```

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