Matrix inverse (inv) in SciPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function that calculates the inverse of a matrix.

SciPy

from scipy.linalg import [1]

matrix = [[1, 2], [3, 4]]
inv_matrix = inv(matrix)
print(inv_matrix)

Drag options to blanks, or click blank then click option'

Ainverse

Binv_matrix

Cinvert

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'inverse' instead of 'inv'.

Trying to import a non-existing function like 'invert'.

The function to calculate the inverse of a matrix in scipy.linalg is inv.

2fill in blank

medium

Complete the code to create a 2x2 numpy array matrix.

SciPy

import numpy as np

matrix = np.array([1])
print(matrix)

Drag options to blanks, or click blank then click option'

A[[1, 3], [2, 4]]

B[1, 2, 3, 4]

C[[1, 2], [3, 4]]

D[[1, 2, 3], [4, 5, 6]]

Attempts:

3 left

💡 Hint

Common Mistakes

Using a flat list instead of nested lists.

Using wrong dimensions like 2x3.

A 2x2 matrix is a list of two lists, each with two elements, like [[1, 2], [3, 4]].

3fill in blank

hard

Fix the error in the code to correctly calculate the inverse of the matrix.

SciPy

from scipy.linalg import inv
import numpy as np

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

Drag options to blanks, or click blank then click option'

Ainv

Binv_matrix

Cinvert

Dinverse

Attempts:

3 left

💡 Hint

Common Mistakes

Using 'inverse' or 'invert' which are not defined.

Trying to call the variable name as a function.

The correct function to calculate the inverse is inv, not 'inverse' or 'invert'.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each element to its inverse value.

SciPy

matrix = [1, 2, 4, 5]
inverse_map = { [1]: 1/[2] for [1] in matrix }
print(inverse_map)

Drag options to blanks, or click blank then click option'

Ax

Bi

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names before colon and after 'for'.

Using variable names not defined in the comprehension.

In dictionary comprehension, the variable name before the colon and after 'for' must be the same. Here, 'x' is used consistently.

5fill in blank

hard

Fill all three blanks to create a dictionary comprehension that maps each number to its inverse if the number is not zero.

SciPy

numbers = [1, 2, 0, 4]
inverse_dict = { [1]: 1/[2] for [3] in numbers if [2] != 0 }
print(inverse_dict)

Drag options to blanks, or click blank then click option'

Anum

Dn

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names causing NameError.

Not checking for zero before division.

Use the same variable name 'num' consistently in the comprehension for clarity and correctness.

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