np.linalg.inv() for matrix inverse in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the numpy library with the common alias.

NumPy

import [1] as np

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

Anumpy

Bpandas

Cmatplotlib

Dscipy

Attempts:

3 left

💡 Hint

Common Mistakes

Importing the wrong library like pandas or matplotlib.

Not using the alias np.

We import the numpy library as np to use its functions easily.

2fill in blank

medium

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

NumPy

matrix = np.array([1])

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

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

B[1, 2, 3, 4]

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

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

Attempts:

3 left

💡 Hint

Common Mistakes

Using a flat list instead of nested lists.

Creating a matrix with wrong dimensions.

The matrix must be a 2x2 nested list to create a 2D numpy array.

3fill in blank

hard

Fix the error in the code to compute the inverse of the matrix.

NumPy

inverse = np.linalg.[1](matrix)

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

Aeig

Bdet

Csolve

Dinv

Attempts:

3 left

💡 Hint

Common Mistakes

Using det which computes determinant, not inverse.

Using solve which solves linear systems.

The function np.linalg.inv() computes the inverse of a matrix.

4fill in blank

hard

Fill both blanks to create a dictionary with keys as matrix elements and values as their inverses.

NumPy

inverse_dict = {element: [1] for row in matrix for element in row if element [2] 0}

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A1/element

Belement

C==

D!=

Attempts:

3 left

💡 Hint

Common Mistakes

Using equality check instead of inequality in the condition.

Not handling zero elements causing division by zero.

We calculate the inverse of each element by dividing 1 by it, and skip zero elements to avoid division errors.

5fill in blank

hard

Fill all three blanks to compute the inverse matrix and print it.

NumPy

import numpy as np
matrix = np.array([1])
inverse = np.linalg.[2](matrix)
print([3])

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A[[2, 0], [0, 2]]

Binv

Cinverse

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

Attempts:

3 left

💡 Hint

Common Mistakes

Using the wrong matrix shape.

Calling a wrong function instead of inv.

Printing the original matrix instead of the inverse.

We create a 2x2 matrix, compute its inverse using np.linalg.inv(), and print the inverse matrix.

Practice

1. What does the function np.linalg.inv() do in numpy?

easy

A. It calculates the inverse of a square matrix.

B. It computes the determinant of a matrix.

C. It transposes a matrix.

D. It multiplies two matrices.

Solution

1. Step 1: Understand the function purpose

   np.linalg.inv() is designed to find the inverse of a matrix, which is a matrix that when multiplied with the original gives the identity matrix.

2. Step 2: Differentiate from other matrix operations

   Calculating determinant, transpose, or multiplication are different functions in numpy, not np.linalg.inv().

3. Final Answer:

   It calculates the inverse of a square matrix. -> Option A

4. Quick Check:

   np.linalg.inv() = inverse matrix [OK]

Hint: Inverse matrix means undo multiplication [OK]

Common Mistakes:

• Confusing inverse with transpose
• Thinking it calculates determinant
• Assuming it multiplies matrices

2. Which of the following is the correct syntax to find the inverse of a matrix A using numpy?

easy

A. np.inv(A)

B. np.linalg.inverse(A)

C. np.linalg.inv(A)

D. np.inverse(A)

Solution

1. Step 1: Recall numpy linear algebra module

   The inverse function is inside the linalg module of numpy, so it must be called as np.linalg.inv().

2. Step 2: Check function names

   Functions like np.inv(), np.inverse(), or np.linalg.inverse() do not exist in numpy.

3. Final Answer:

   np.linalg.inv(A) -> Option C

4. Quick Check:

   Correct syntax = np.linalg.inv(A) [OK]

Hint: Use np.linalg.inv() for matrix inverse [OK]

Common Mistakes:

• Omitting 'linalg' module
• Using wrong function names
• Confusing with np.inverse()

3. You have a matrix C = np.array([[2, 3], [1, 4]]). You want to verify that np.linalg.inv(C) is correct by multiplying C with its inverse. What should the result be?

easy

A. An identity matrix of the same size as C.

B. The original matrix C itself.

C. A zero matrix of the same size as C.

D. A matrix with all elements equal to 1.

Solution

1. Step 1: Recall property of inverse matrices

   Multiplying a matrix by its inverse results in the identity matrix, which has 1s on the diagonal and 0s elsewhere.

2. Step 2: Apply to matrix C

   So, C @ np.linalg.inv(C) should produce the identity matrix of size 2x2.

3. Final Answer:

   An identity matrix of the same size as C. -> Option A

4. Quick Check:

   Matrix x inverse = identity matrix [OK]

Hint: Matrix times inverse equals identity [OK]

Common Mistakes:

• Expecting zero matrix instead
• Confusing with original matrix
• Thinking result is all ones

4. What is the output of the following code?

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

medium

A. [[ 4. -2. ]
[-3. 1.5]]

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

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

D. [[ 0.5 -0.25]
[-0.75 0.25]]

Solution

1. Step 1: Calculate determinant of A

   Determinant = (1*4) - (2*3) = 4 - 6 = -2.

2. Step 2: Compute inverse using formula

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

3. Step 3: Check numpy output

   Numpy returns approximately [[-2., 1.], [1.5, -0.5]]. np.round(inv_A, 2) prints as [[-2. 1. ] [ 1.5 -0.5]], matching [[-2. 1. ] [ 1.5 -0.5]].

4. Final Answer:

   [[ 0.5 -0.25] [-0.75 0.25]] -> Option D

5. Quick Check:

   np.linalg.inv(A) rounded = [[ 0.5 -0.25] [-0.75 0.25]] [OK]

Hint: Inverse = adjoint / determinant [OK]

Common Mistakes:

• Confusing determinant sign
• Not rounding output
• Mixing up matrix elements

5. What is the error in the following code snippet?

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

medium

A. TypeError because np.linalg.inv() expects a list.

B. ValueError because B is not a square matrix.

C. SyntaxError due to missing parentheses.

D. No error; code runs fine.

Solution

1. Step 1: Check matrix shape

   Matrix B has shape (2, 3), which is not square (rows != columns).

2. Step 2: Understand np.linalg.inv() requirements

   np.linalg.inv() requires a square matrix to compute the inverse. Non-square matrices cannot have inverses.

3. Final Answer:

   ValueError because B is not a square matrix. -> Option B

4. Quick Check:

   Non-square matrix = ValueError [OK]

Hint: Inverse only for square matrices [OK]

Common Mistakes:

• Trying inverse on non-square matrix
• Confusing error type
• Assuming code runs without error