# 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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