Creating a 3x3 array and computing QR decomposition using NumPy

NumPy: Advanced Exercise-27 with Solution

Write a NumPy program to create a 3x3 array with random values and compute the QR decomposition.

QR decomposition is a factorization of a matrix into an orthogonal matrix 𝑄 and an upper triangular matrix 𝑅. In NumPy, the numpy.linalg.qr() function computes the QR decomposition of a given matrix. It's often used in numerical linear algebra for solving linear least squares problems, eigenvalue problems, and many other applications.

Sample Solution:

Python Code:

import numpy as np

# Create a 3x3 array with random values
array = np.random.random((3, 3))

# Compute the QR decomposition
q, r = np.linalg.qr(array)

# Print the original array, Q matrix, and R matrix
print("Original Array:\n", array)
print("Q Matrix:\n", q)
print("R Matrix:\n", r)

Output:

Original Array:
 [[0.86640332 0.76640485 0.65182287]
 [0.30254272 0.92296395 0.82323944]
 [0.31141372 0.21789583 0.88200149]]
Q Matrix:
 [[-0.89402381  0.26365732 -0.36222402]
 [-0.31218763 -0.9465117   0.08157502]
 [-0.32134143  0.18601187  0.92851455]]
R Matrix:
 [[-0.96910542 -1.04334106 -1.12317395]
 [ 0.         -0.63099672 -0.44328514]
 [ 0.          0.          0.65000109]]

Explanation:

• Import NumPy: Import the NumPy library to work with arrays.
• Create a Random 3x3 Array: Generate a 3x3 array filled with random values using np.random.random.
• Compute QR Decomposition: Use np.linalg.qr to compute the QR decomposition of the array.
• Print Results: Print the original array, the Q matrix, and the R matrix resulting from the QR decomposition.

Python-Numpy Code Editor:

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