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Solve Linear algebra problems with NumPy and SciPy

NumPy: Integration with SciPy Exercise-3 with Solution

Write a NumPy program that creates a NumPy array and uses SciPy to solve a linear algebra problem. For example, finding the determinant, inverse, and eigenvalues of a matrix.

Sample Solution:

Python Code:

# Import necessary libraries
import numpy as np
from scipy import linalg

# Create a NumPy array (matrix)
matrix = np.array([[4, 2], [3, 1]])

# Find the determinant of the matrix using SciPy
determinant = linalg.det(matrix)

# Find the inverse of the matrix using SciPy
inverse = linalg.inv(matrix)

# Find the eigenvalues of the matrix using SciPy
eigenvalues, eigenvectors = linalg.eig(matrix)

# Print the matrix
print("Matrix:")
print(matrix)

# Print the determinant of the matrix
print("Determinant:")
print(determinant)

# Print the inverse of the matrix
print("Inverse:")
print(inverse)

# Print the eigenvalues of the matrix
print("Eigenvalues:")
print(eigenvalues)

# Print the eigenvectors of the matrix
print("Eigenvectors:")
print(eigenvectors)

Output:

Matrix:
[[4 2]
 [3 1]]
Determinant:
-2.0
Inverse:
[[-0.5  1. ]
 [ 1.5 -2. ]]
Eigenvalues:
[ 5.37228132+0.j -0.37228132+0.j]
Eigenvectors:
[[ 0.82456484 -0.41597356]
 [ 0.56576746  0.90937671]]

Explanation:

  • Import necessary libraries:
    • Import NumPy and SciPy's linalg module for linear algebra functions.
  • Create a NumPy array (matrix):
    • Define a 2x2 matrix.
  • Find the determinant of the matrix:
    • Use SciPy's det function to compute the determinant.
  • Find the inverse of the matrix:
    • Use SciPy's inv function to compute the inverse.
  • Find the eigenvalues and eigenvectors of the matrix:
    • Use SciPy's eig function to compute the eigenvalues and eigenvectors.
  • Print the matrix:
    • Display the original matrix.
  • Print the determinant of the matrix:
    • Display the determinant.
  • Print the inverse of the matrix:
    • Display the inverse.
  • Print the eigenvalues of the matrix:
    • Display the eigenvalues.
  • Print the eigenvectors of the matrix: Display the eigenvectors.

Python-Numpy Code Editor: