LU decomposition in SciPy - Mini Project: Build & Apply

LU Decomposition with SciPy

📖 Scenario: You work as a data analyst and need to solve systems of linear equations quickly. LU decomposition helps break down a matrix into simpler parts to make solving easier.

🎯 Goal: Learn how to perform LU decomposition on a matrix using SciPy and understand the output matrices.

📋 What You'll Learn

Create a 3x3 matrix using NumPy

Set up a configuration variable for the matrix size

Use SciPy's LU decomposition function to decompose the matrix

Print the resulting matrices from the decomposition

💡 Why This Matters

🌍 Real World

LU decomposition is used in engineering and data science to solve systems of equations efficiently, such as in simulations or optimization problems.

💼 Career

Understanding LU decomposition helps in roles involving numerical analysis, scientific computing, and data modeling where matrix operations are common.

1

Create the matrix

Create a NumPy array called matrix with these exact values: [[4, 3, 2], [3, 2, 1], [2, 1, 3]].

SciPy

# Create the matrix variable with the given values
# Your code here

Need a hint?

Use np.array to create the matrix with the exact values.

2

Set matrix size variable

Create a variable called size and set it to 3 to represent the matrix size.

SciPy

import numpy as np

matrix = np.array([[4, 3, 2], [3, 2, 1], [2, 1, 3]])

# Create the size variable and set it to 3
# Your code here

Need a hint?

Just assign the number 3 to the variable size.

3

Perform LU decomposition

Import lu from scipy.linalg and use it to decompose matrix into P, L, and U matrices.

SciPy

import numpy as np

matrix = np.array([[4, 3, 2], [3, 2, 1], [2, 1, 3]])

size = 3

# Import lu and perform LU decomposition
# Your code here

Need a hint?

Use from scipy.linalg import lu and then call lu(matrix).

4

Print the results

Print the matrices P, L, and U each on a separate line.

SciPy

import numpy as np
from scipy.linalg import lu

matrix = np.array([[4, 3, 2], [3, 2, 1], [2, 1, 3]])

size = 3

P, L, U = lu(matrix)

# Print P, L, and U matrices
# Your code here

Need a hint?

Use three print statements, one for each matrix: P, L, and U.