Matrix creation and operations in SciPy - Mini Project: Build & Apply

Matrix creation and operations

📖 Scenario: You are working as a data analyst and need to create and manipulate matrices to analyze data patterns. Matrices are like grids of numbers, similar to tables you see in spreadsheets.

🎯 Goal: Build a small project where you create a matrix using scipy, set a configuration value for matrix size, perform a matrix operation (like addition), and then display the result.

📋 What You'll Learn

Use scipy to create matrices

Create a matrix with exact values

Set a configuration variable for matrix size

Perform matrix addition using scipy

Print the resulting matrix

💡 Why This Matters

🌍 Real World

Matrices are used in data science to represent data tables, images, and networks. Sparse matrices help save memory when data has many zeros.

💼 Career

Understanding matrix operations is essential for roles in data analysis, machine learning, and scientific computing.

1

Create a 2x2 matrix using scipy

Import scipy.sparse and create a 2x2 matrix called matrix_a with these exact values: [[1, 2], [3, 4]] using scipy.sparse.csr_matrix.

SciPy

# Your code here

Hint

Use csr_matrix from scipy.sparse to create the matrix.

2

Set matrix size configuration

Create a variable called matrix_size and set it to 2 to represent the size of the matrix.

SciPy

from scipy.sparse import csr_matrix
matrix_a = csr_matrix([[1, 2], [3, 4]])
# Your code here

Hint

Just create a variable matrix_size and assign it the value 2.

3

Create another matrix and add it to the first

Create another 2x2 matrix called matrix_b with values [[5, 6], [7, 8]] using csr_matrix. Then create a new matrix called matrix_sum by adding matrix_a and matrix_b.

SciPy

from scipy.sparse import csr_matrix
matrix_a = csr_matrix([[1, 2], [3, 4]])
matrix_size = 2
# Your code here

Hint

Create matrix_b like matrix_a but with new values, then add them with matrix_sum = matrix_a + matrix_b.

4

Print the resulting matrix

Print the dense array form of matrix_sum using the .toarray() method inside a print() statement.

SciPy

from scipy.sparse import csr_matrix
matrix_a = csr_matrix([[1, 2], [3, 4]])
matrix_size = 2
matrix_b = csr_matrix([[5, 6], [7, 8]])
matrix_sum = matrix_a + matrix_b
# Your code here

Hint

Use print(matrix_sum.toarray()) to see the full matrix.

Practice

1. What does the scipy.linalg.inv() function do when applied to a square matrix?

easy

A. Transposes the matrix

B. Calculates the determinant of the matrix

C. Calculates the inverse of the matrix

D. Creates a zero matrix of the same size

Solution

1. Step 1: Understand the function purpose

   The scipy.linalg.inv() function is designed to find the inverse of a square matrix if it exists.

2. Step 2: Differentiate from other matrix operations

   Determinant calculation uses scipy.linalg.det(), transpose uses .T, and zero matrix creation uses numpy.zeros().

3. Final Answer:

   Calculates the inverse of the matrix -> Option C

4. Quick Check:

   Inverse = inv() [OK]

Hint: Inverse means flipping matrix; use inv() for that [OK]

Common Mistakes:

• Confusing inverse with determinant
• Thinking inv() transposes matrix
• Assuming inv() creates zero matrix

2. Which of the following is the correct way to create a 3x3 identity matrix using NumPy?

easy

A. scipy.identity(3)

B. scipy.eye(3)

C. scipy.linalg.eye(3)

D. np.identity(3)

Solution

1. Step 1: Identify the correct module and function

   The identity matrix function is in numpy (imported as np) as identity().

2. Step 2: Check other options for correctness

   scipy.eye() and scipy.linalg.eye() do not exist; scipy.identity() is not valid.

3. Final Answer:

   np.identity(3) -> Option D

4. Quick Check:

   Identity matrix = np.identity() [OK]

Hint: Use np.identity() for identity matrix [OK]

Common Mistakes:

• Using scipy.eye() which does not exist
• Calling identity() from wrong module
• Confusing identity with eye from numpy

3. What is the output of the following code?

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

medium

A. -2.00

B. 2.00

C. 10.00

D. -10.00

Solution

1. Step 1: Calculate determinant of matrix A

   Determinant formula for 2x2 matrix [[a,b],[c,d]] is ad - bc = 1*4 - 2*3 = 4 - 6 = -2.

2. Step 2: Round the result to 2 decimals

   Rounding -2 to 2 decimals remains -2.00.

3. Final Answer:

   -2.00 -> Option A

4. Quick Check:

   Determinant = -2.00 [OK]

Hint: Determinant 2x2 = ad - bc [OK]

Common Mistakes:

• Calculating ad + bc instead of ad - bc
• Forgetting negative sign
• Not rounding output

4. Identify the error in this code snippet:

import numpy as np
from scipy.linalg import inv
B = np.array([[1, 2], [2, 4]])
B_inv = inv(B)
print(B_inv)

medium

A. Matrix B is singular and cannot be inverted

B. Syntax error in array creation

C. inv() function is not imported correctly

D. Matrix B is not square

Solution

1. Step 1: Check matrix properties

   Matrix B is square (2x2), but rows are linearly dependent (second row is twice the first).

2. Step 2: Understand invertibility

   Such a matrix is singular (determinant zero), so inverse does not exist, causing an error when calling inv().

3. Final Answer:

   Matrix B is singular and cannot be inverted -> Option A

4. Quick Check:

   Singular matrix = no inverse [OK]

Hint: Check determinant; zero means no inverse [OK]

Common Mistakes:

• Thinking non-square matrix causes error here
• Assuming inv() import is wrong
• Missing linear dependence in matrix

5. You have two matrices:

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

Which code correctly computes the product P = M x N using scipy?

hard

A. from scipy.linalg import dot
P = dot(M, N)

B. import numpy as np
P = np.dot(M, N)

C. from scipy.linalg import matmul
P = matmul(M, N)

D. from scipy.linalg import inv
P = inv(M) * N

Solution

1. Step 1: Identify correct matrix multiplication function

   Scipy.linalg does not have dot or matmul functions; numpy provides np.dot() for matrix multiplication.

2. Step 2: Check options for correctness

   import numpy as np P = np.dot(M, N) uses np.dot(M, N) which correctly multiplies matrices M and N. from scipy.linalg import inv P = inv(M) * N incorrectly uses inverse and element-wise multiplication.

3. Final Answer:

   import numpy as np P = np.dot(M, N) -> Option B

4. Quick Check:

   Matrix product = np.dot() [OK]

Hint: Use np.dot() for matrix multiplication [OK]

Common Mistakes:

• Using inv() instead of multiplication
• Assuming scipy.linalg has dot or matmul
• Using * for matrix multiplication