Matrix inverse (inv) in SciPy - Mini Project: Build & Apply

Matrix inverse (inv)

📖 Scenario: You work as a data analyst and need to solve a system of equations using matrix operations. One important step is to find the inverse of a matrix.

🎯 Goal: Learn how to create a matrix using numpy and find its inverse using scipy.linalg.inv.

📋 What You'll Learn

Create a 2x2 matrix using numpy.array with exact values

Import the inv function from scipy.linalg

Calculate the inverse of the matrix using inv

Print the inverse matrix

💡 Why This Matters

🌍 Real World

Matrix inversion is used in many fields like engineering, physics, and computer science to solve systems of equations and transform data.

💼 Career

Knowing how to invert matrices is important for data analysts and scientists working with linear algebra problems and machine learning algorithms.

1

Create the matrix

Create a variable called matrix and assign it a 2x2 numpy array with these exact values: [[4, 7], [2, 6]].

SciPy

# Your code here

Hint

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

2

Import the inverse function

Import the inv function from scipy.linalg.

SciPy

import numpy as np
matrix = np.array([[4, 7], [2, 6]])
# Your code here

Hint

Use from scipy.linalg import inv to import the inverse function.

3

Calculate the inverse matrix

Create a variable called inverse_matrix and assign it the inverse of matrix using the inv function.

SciPy

import numpy as np
matrix = np.array([[4, 7], [2, 6]])
from scipy.linalg import inv
# Your code here

Hint

Use inv(matrix) to calculate the inverse.

4

Print the inverse matrix

Print the variable inverse_matrix to display the inverse matrix.

SciPy

import numpy as np
matrix = np.array([[4, 7], [2, 6]])
from scipy.linalg import inv
inverse_matrix = inv(matrix)
# Your code here

Hint

Use print(inverse_matrix) to show the result.

Practice

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

easy

A. It computes the determinant of the matrix.

B. It calculates the inverse of a square, non-singular matrix.

C. It transposes the matrix.

D. It multiplies the matrix by itself.

Solution

1. Step 1: Understand the purpose of scipy.linalg.inv

   This function is designed to find the inverse of a matrix, which is a matrix that when multiplied by the original gives the identity matrix.

2. Step 2: Identify the matrix requirements

   The matrix must be square (same number of rows and columns) and non-singular (determinant not zero) to have an inverse.

3. Final Answer:

   It calculates the inverse of a square, non-singular matrix. -> Option B

4. Quick Check:

   Inverse matrix = calculated by inv [OK]

Hint: Inverse = reverse matrix effect, only for square non-singular [OK]

Common Mistakes:

• Confusing inverse with transpose
• Trying to invert non-square matrices
• Assuming singular matrices have inverses

2. Which of the following is the correct way to import and use the inverse function from scipy?

easy

A. import inv from scipy.linalg
matrix_inv = inv(matrix)

B. import scipy.linalg
matrix_inv = scipy.linalg.inverse(matrix)

C. from scipy import inv
matrix_inv = inv(matrix)

D. from scipy.linalg import inv
matrix_inv = inv(matrix)

Solution

1. Step 1: Recall correct import syntax

   The function inv is inside scipy.linalg, so we import it using from scipy.linalg import inv.

2. Step 2: Use the function correctly

   After import, call inv(matrix) to get the inverse.

3. Final Answer:

   from scipy.linalg import inv matrix_inv = inv(matrix) -> Option D

4. Quick Check:

   Correct import and call = from scipy.linalg import inv matrix_inv = inv(matrix) [OK]

Hint: Import inv from scipy.linalg, then call inv(matrix) [OK]

Common Mistakes:

• Using wrong function name like 'inverse'
• Incorrect import syntax
• Trying to import inv directly from scipy

3. What is the output of this code?

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

medium

A. [[ -2. 1. ]
[ 1.5 -0.5]]

B. [[ 4. -2. ]
[-3. 1. ]]

C. [[ 0.25 0.5 ]
[ 0.75 1. ]]

D. [[ 1.5 -1. ]
[-1.5 1. ]]

Solution

1. Step 1: Calculate determinant of the matrix

   Determinant = (1*4) - (2*3) = 4 - 6 = -2 (non-zero, so invertible).

2. Step 2: Compute inverse using formula

   Inverse = (1/det) * [[d, -b], [-c, a]] = (1/-2) * [[4, -2], [-3, 1]] = [[-2, 1], [1.5, -0.5]].

3. Final Answer:

   [[ -2. 1. ] [ 1.5 -0.5]] -> Option A

4. Quick Check:

   Inverse matrix matches [[ -2. 1. ] [ 1.5 -0.5]] [OK]

Hint: Use formula inverse = 1/det * adjugate for 2x2 matrices [OK]

Common Mistakes:

• Mixing up signs in the inverse formula
• Not rounding output
• Confusing transpose with inverse

4. Identify the error in this code snippet:

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

medium

A. Matrix is not square, so it cannot be inverted.

B. Missing import statement for numpy.

C. Using inv instead of inv().

D. Matrix contains integers instead of floats.

Solution

1. Step 1: Check matrix shape

   The matrix has shape (2, 3), which is not square (rows ≠ columns).

2. Step 2: Understand inverse requirements

   Only square matrices can have an inverse. Trying to invert a non-square matrix causes an error.

3. Final Answer:

   Matrix is not square, so it cannot be inverted. -> Option A

4. Quick Check:

   Non-square matrix = no inverse [OK]

Hint: Only square matrices can be inverted [OK]

Common Mistakes:

• Ignoring matrix shape
• Assuming all matrices are invertible
• Confusing function call syntax

5. You have a 3x3 matrix A and want to solve the system Ax = b for x. Which approach using scipy.linalg.inv is correct and efficient?

hard

A. Calculate inv(A) and then multiply by b to get x.

B. Transpose A and multiply by b to get x.

C. Directly compute x = scipy.linalg.solve(A, b) without using inverse.

D. Use np.dot(A, b) to find x.

Solution

1. Step 1: Understand solving linear systems

   To solve Ax = b, the best practice is to use specialized solvers like scipy.linalg.solve which are optimized and more stable.

2. Step 2: Compare with inverse method

   Calculating inv(A) and then multiplying by b is less efficient and can introduce numerical errors.

3. Final Answer:

   Directly compute x = scipy.linalg.solve(A, b) without using inverse. -> Option C

4. Quick Check:

   Use solve() for linear systems, not inv() [OK]

Hint: Use solve() for Ax=b, avoid explicit inverse [OK]

Common Mistakes:

• Using inverse for solving linear systems
• Confusing transpose with inverse
• Multiplying matrices incorrectly