Matrix determinant (det) in SciPy - Mini Project: Build & Apply

Calculate Matrix Determinant Using SciPy

📖 Scenario: You work as a data analyst and need to find the determinant of a matrix to understand its properties. The determinant helps in solving systems of linear equations and checking if a matrix is invertible.

🎯 Goal: Build a Python program that creates a matrix, sets up the necessary configuration, calculates the determinant using SciPy, and prints the result.

📋 What You'll Learn

Create a 3x3 matrix with exact values

Import the required function from SciPy

Calculate the determinant of the matrix

Print the determinant value

💡 Why This Matters

🌍 Real World

Determinants are used in engineering and data science to check if systems of equations have unique solutions and to analyze matrix properties.

💼 Career

Knowing how to calculate determinants is useful for roles involving linear algebra, such as data scientists, machine learning engineers, and researchers.

1

Create the matrix

Create a variable called matrix and assign it a 3x3 list of lists with these exact values: [[4, 2, 3], [3, 1, 5], [1, 0, 2]].

SciPy

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

Hint

Use a list of lists to represent the matrix rows and columns exactly as shown.

2

Import the determinant function

Import the det function from the scipy.linalg module.

SciPy

matrix = [[4, 2, 3], [3, 1, 5], [1, 0, 2]]
# Import det from scipy.linalg
# Your code here

Hint

Use the exact import statement: from scipy.linalg import det.

3

Calculate the determinant

Create a variable called determinant and assign it the result of calling det(matrix).

SciPy

matrix = [[4, 2, 3], [3, 1, 5], [1, 0, 2]]
from scipy.linalg import det
# Calculate the determinant of matrix
# Your code here

Hint

Call det(matrix) and store the result in determinant.

4

Print the determinant

Print the value of the variable determinant.

SciPy

matrix = [[4, 2, 3], [3, 1, 5], [1, 0, 2]]
from scipy.linalg import det
determinant = det(matrix)
# Print the determinant
# Your code here

Hint

Use print(determinant) to show the result.

Practice

1. What does the determinant of a square matrix tell us in simple terms?

easy

A. If the matrix can be reversed or undone

B. The number of rows in the matrix

C. The sum of all elements in the matrix

D. The largest value in the matrix

Solution

1. Step 1: Understand determinant meaning

   The determinant helps us know if a matrix can be inverted or reversed.

2. Step 2: Relate to matrix properties

   If the determinant is zero, the matrix cannot be inverted; otherwise, it can.

3. Final Answer:

   If the matrix can be reversed or undone -> Option A

4. Quick Check:

   Determinant shows invertibility [OK]

Hint: Determinant zero means no inverse [OK]

Common Mistakes:

• Confusing determinant with matrix size
• Thinking determinant is sum of elements
• Assuming determinant gives max value

2. Which of the following is the correct way to import the determinant function from scipy?

easy

A. from scipy import determinant

B. from scipy.linalg import det

C. import scipy.det

D. import det from scipy.linalg

Solution

1. Step 1: Recall scipy.linalg module usage

   The determinant function is in scipy.linalg and is named det.

2. Step 2: Check correct import syntax

   Python import syntax for a function is: from module import function.

3. Final Answer:

   from scipy.linalg import det -> Option B

4. Quick Check:

   Correct import syntax for det [OK]

Hint: Use 'from scipy.linalg import det' to import [OK]

Common Mistakes:

• Using wrong module name
• Incorrect import syntax
• Trying to import non-existent names

3. What is the output of this code?

import numpy as np
from scipy.linalg import det
A = np.array([[2, 3], [1, 4]])
print(round(det(A), 2))

medium

A. 14.0

B. 10.0

C. 11.0

D. 5.0

Solution

1. Step 1: Calculate determinant manually

   For matrix [[2,3],[1,4]], determinant = (2*4) - (3*1) = 8 - 3 = 5.

2. Step 2: Confirm code output

   Code prints determinant rounded to 2 decimals, so output is 5.0.

3. Final Answer:

   5.0 -> Option D

4. Quick Check:

   Determinant = 5.0 [OK]

Hint: Det = ad - bc for 2x2 matrix [OK]

Common Mistakes:

• Mixing multiplication order
• Not rounding output
• Confusing matrix elements

4. Identify the error in this code snippet:

import numpy as np
from scipy.linalg import det
B = np.array([[1, 2, 3], [4, 5, 6]])
print(det(B))

medium

A. Matrix B is not square, so det() will raise an error

B. Missing import for numpy

C. det() function is misspelled

D. No error, code runs fine

Solution

1. Step 1: Check matrix shape

   Matrix B has shape (2,3), which is not square.

2. Step 2: Understand det() requirements

   det() requires a square matrix; otherwise, it raises a LinAlgError.

3. Final Answer:

   Matrix B is not square, so det() will raise an error -> Option A

4. Quick Check:

   det() needs square matrix [OK]

Hint: Only square matrices have determinants [OK]

Common Mistakes:

• Ignoring matrix shape
• Assuming det works on any matrix
• Overlooking error messages

5. You have a 3x3 matrix:

M = np.array([[1, 2, 3], [0, 1, 4], [5, 6, 0]])

Using scipy.linalg.det, what is the determinant of M? Choose the closest value rounded to 2 decimals.

hard

A. -24.00

B. 31.00

C. 1.00

D. -79.00

Solution

1. Step 1: Calculate determinant manually

   Calculate determinant of M:
   det(M) = 1*(1*0 - 4*6) - 2*(0*0 - 4*5) + 3*(0*6 - 1*5)
   = 1*(0 - 24) - 2*(0 - 20) + 3*(0 - 5)
   = -24 + 40 - 15 = 1

2. Step 2: Confirm with scipy.linalg.det

   Using det(M) in code returns 1.0, rounded to 2 decimals is 1.00.

3. Final Answer:

   1.00 -> Option C

4. Quick Check:

   Determinant = 1.00 [OK]

Hint: Use cofactor expansion for 3x3 determinant [OK]

Common Mistakes:

• Wrong sign in cofactor terms
• Mixing row and column indices
• Forgetting to round result