How To Solve A Matrix In Python

In this tutorial, we will learn how to solve a matrix in Python using the popular numerical computation library called NumPy. Solving a matrix means finding the values of the variables from the given linear equations. We will be focusing on systems of linear equations that have unique solutions.

Before we proceed, make sure you have the NumPy library installed in your Python environment. If not, you can install it using the following command:

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pip install numpy

Let’s start solving a matrix using some simple steps.

Step 1: Define Your Problem

First, you need to define the linear equations that form the matrix. For example, let’s consider the following system of linear equations:

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x + y + z = 6
2y + 5z = -4
2x + 5y - z = 27

Step 2: Convert the Equations to Matrices

Now, we need to convert the linear system into two matrices: the coefficient matrix and the constant matrix.

The coefficient matrix contains the coefficients of the variables. For our example, the coefficient matrix is:

| 1 1 1 |
| 0 2 5 |
| 2 5 -1 |

The constant matrix contains the constants on the right side of the equal signs. For our example, the constant matrix is:

| 6 |
| -4 |
| 27 |

Step 3: Use NumPy to Solve the Matrix

Now, let’s use NumPy to solve the matrix. First, we need to import the NumPy library. Then we will create our coefficient and constant matrices using the numpy.array() function. Finally, we will use the numpy.linalg.solve() function to solve the matrix and find the values of x, y, and z.

Here’s the code:

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import numpy as np
 
# Create the coefficient matrix
coeff_matrix = np.array([[1, 1, 1],
                         [0, 2, 5],
                         [2, 5, -1]])
 
# Create the constant matrix
const_matrix = np.array([6, -4, 27])
 
# Solve the matrix
solution = np.linalg.solve(coeff_matrix, const_matrix)
 
print(coeff_matrix, '\n')
print(const_matrix, '\n')
print(solution)
 

When you run this code, the solution variable will now contain the values of x, y, and z that satisfy the linear system of equations.

Here’s the output:

[ 5.  3. -2.]

So, the values of x, y, and z are 5, 3, and -2, respectively.

Full code:

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import numpy as np
 
# Create the coefficient matrix
coeff_matrix = np.array([[1, 1, 1],
                         [0, 2, 5],
                         [2, 5, -1]])
 
# Create the constant matrix
const_matrix = np.array([6, -4, 27])
 
# Solve the matrix
solution = np.linalg.solve(coeff_matrix, const_matrix)
 
print(solution)

Output:

[[ 1  1  1]
 [ 0  2  5]
 [ 2  5 -1]] 

[ 6 -4 27] 

[ 5.  3. -2.]

Conclusion

By now, you should be familiar with the process of solving a matrix in Python using NumPy. We learned how to define a system of linear equations, convert it into matrices, and use NumPy’s built-in functions to find the solution. We hope you find this tutorial useful, and it helps you in your further applications and problem-solving tasks involving matrix computations.