Matrix transpose operations in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of Transpose on 2D NumPy Array

What is the output of the following code that transposes a 2D NumPy array?

NumPy

import numpy as np
arr = np.array([[1, 2, 3], [4, 5, 6]])
result = arr.T
print(result)

A

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

B

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

C

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

D

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

💡 Hint

Remember that transpose flips rows and columns.

The transpose of a 2x3 matrix becomes a 3x2 matrix where rows become columns.

❓ data_output

intermediate

Shape After Transpose of 3D Array

Given a 3D NumPy array with shape (2, 3, 4), what is the shape after applying arr.transpose(1, 0, 2)?

NumPy

import numpy as np
arr = np.zeros((2, 3, 4))
result = arr.transpose(1, 0, 2)
print(result.shape)

A (3, 2, 4)

B (2, 3, 4)

C (4, 3, 2)

D (3, 4, 2)

💡 Hint

Transpose rearranges axes in the order you specify.

The axes are reordered from (0,1,2) to (1,0,2), so shape changes from (2,3,4) to (3,2,4).

🔧 Debug

advanced

Identify the Error in Transpose Usage

What error does this code raise when trying to transpose a 2D array with an invalid axis order? import numpy as np arr = np.array([[1, 2], [3, 4]]) result = arr.transpose(0, 2) print(result)

NumPy

import numpy as np
arr = np.array([[1, 2], [3, 4]])
result = arr.transpose(0, 2)
print(result)

A No error, prints transposed array

B IndexError: axis 2 is out of bounds for array of dimension 2

C TypeError: transpose() takes no arguments

D ValueError: axes don't match array

💡 Hint

Check the number of dimensions in the array and the axes used.

The array has 2 dimensions (axes 0 and 1). Using axis 2 causes ValueError because axes don't match array.

🚀 Application

advanced

Using Transpose to Swap Rows and Columns in Data

You have a dataset as a NumPy array with shape (5, 10), where rows are samples and columns are features. You want to switch rows and columns to have features as rows and samples as columns. Which code correctly does this?

A All of the above

B np.transpose(data, (1, 0))

C np.swapaxes(data, 0, 1)

D data.T

💡 Hint

All these methods can swap axes 0 and 1 for 2D arrays.

For 2D arrays, .T, np.transpose with axes (1,0), and np.swapaxes(0,1) all swap rows and columns.

🧠 Conceptual

expert

Effect of Transpose on Memory Layout

Which statement best describes the effect of transposing a NumPy array on its memory layout?

A Transpose always creates a new copy of the array with contiguous memory.

B Transpose returns a view with changed strides, no data is copied.

C Transpose modifies the original array in-place to swap rows and columns.

D Transpose converts the array to a list of lists.

💡 Hint

Think about whether transpose copies data or just changes how data is accessed.

Transpose returns a view with modified strides, so no data is copied and memory layout changes logically.

Practice

1. What does the .T attribute do when applied to a NumPy matrix?

easy

A. It flips the rows and columns of the matrix (transpose).

B. It multiplies all elements by 2.

C. It returns the sum of all elements.

D. It flattens the matrix into a 1D array.

Solution

1. Step 1: Understand the .T attribute

   The .T attribute in NumPy returns the transpose of a matrix, which means rows become columns and columns become rows.

2. Step 2: Compare with other options

   Multiplying by 2, summing elements, or flattening are different operations and not related to .T.

3. Final Answer:

   It flips the rows and columns of the matrix (transpose). -> Option A

4. Quick Check:

   Transpose = flip rows and columns [OK]

Hint: Remember: .T flips rows and columns [OK]

Common Mistakes:

• Confusing transpose with flattening
• Thinking .T multiplies elements
• Assuming .T sums elements

2. Which of the following is the correct syntax to transpose a NumPy array named arr?

easy

A. arr.transpose

B. arr.T()

C. transpose(arr)

D. arr.T

Solution

1. Step 1: Recall NumPy transpose syntax

   In NumPy, .T is an attribute, not a method, so it does not use parentheses.

2. Step 2: Evaluate each option

   arr.transpose() uses transpose() method which exists but is a method, so requires parentheses. arr.T() incorrectly uses .T() as a method. transpose(arr) is not valid syntax. arr.T correctly uses .T attribute without parentheses.

3. Final Answer:

   arr.T -> Option D

4. Quick Check:

   Transpose attribute = arr.T [OK]

Hint: Use .T without parentheses to transpose [OK]

Common Mistakes:

• Using .T() as if it were a method
• Confusing transpose() method with .T attribute
• Trying to call transpose(arr) without import

3. What is the output of the following code?

import numpy as np
arr = np.array([[1, 2], [3, 4]])
print(arr.T)

medium

A. [[1 3]
[2 4]]

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

C. [[4 3]
[2 1]]

D. [[1 4]
[2 3]]

Solution

1. Step 1: Understand the original array

   The array arr is a 2x2 matrix: [[1, 2], [3, 4]].

2. Step 2: Apply transpose operation

   Transposing swaps rows and columns, so the first row [1, 2] becomes the first column, and the second row [3, 4] becomes the second column. Result: [[1, 3], [2, 4]].

3. Final Answer:

   [[1 3] [2 4]] -> Option A

4. Quick Check:

   Transpose swaps rows and columns = [[1 3] [2 4]] [OK]

Hint: Transpose swaps rows and columns positions [OK]

Common Mistakes:

• Confusing transpose with reversing elements
• Mixing rows and columns incorrectly
• Expecting original array output

4. Identify the error in this code snippet that tries to transpose a NumPy array:

import numpy as np
arr = np.array([[1, 2], [3, 4]])
transposed = arr.T()
print(transposed)

medium

A. Array creation syntax is wrong.

B. Using parentheses with .T attribute causes an error.

C. Missing import statement for numpy.

D. print() function is used incorrectly.

Solution

1. Step 1: Check usage of .T

   The .T attribute is not a function, so it should not have parentheses. Using .T() causes a TypeError.

2. Step 2: Verify other parts of the code

   Array creation and import are correct. The print statement is also correct.

3. Final Answer:

   Using parentheses with .T attribute causes an error. -> Option B

4. Quick Check:

   .T is attribute, not method [OK]

Hint: Do not add () after .T attribute [OK]

Common Mistakes:

• Calling .T as a function with ()
• Assuming .T needs import
• Thinking print syntax is wrong

5. You have a 3x2 NumPy array arr = np.array([[1, 2], [3, 4], [5, 6]]). You want to multiply it by another array so that the result is a 2x2 matrix. Which of the following correctly uses transpose to achieve this multiplication?

import numpy as np
arr = np.array([[1, 2], [3, 4], [5, 6]])
arr2 = ???
result = np.dot(arr.T, arr2)
print(result)

hard

A. arr2 = np.array([[1, 0, 1], [0, 1, 1]])

B. arr2 = np.array([[1, 0], [0, 1]])

C. arr2 = np.array([[1, 0], [0, 1], [1, 1]])

D. arr2 = np.array([[1, 0], [0, 1], [1, 1], [0, 0]])

Solution

1. Step 1: Understand shapes of arrays

   arr is 3x2. Its transpose arr.T is 2x3. For matrix multiplication np.dot(arr.T, arr2), the number of rows in arr2 must be 3 to match arr.T's columns.

2. Step 2: Check options for correct shape

   arr2 = np.array([[1, 0], [0, 1], [1, 1]]) shape is 3x2, so arr.T (2x3) dot arr2 (3x2) results in 2x2 matrix, which is valid. arr2 = np.array([[1, 0], [0, 1]]) shape is 2x2, which does not match for multiplication with 2x3. arr2 = np.array([[1, 0, 1], [0, 1, 1]]) shape is 2x3, which does not match. arr2 = np.array([[1, 0], [0, 1], [1, 1], [0, 0]]) shape is 4x2, invalid.

3. Step 3: Re-examine arr2 = np.array([[1, 0], [0, 1]]) carefully

   Actually, arr2 = np.array([[1, 0], [0, 1]]) is 2x2, which cannot multiply with 2x3. So arr2 = np.array([[1, 0], [0, 1], [1, 1]]) is correct.

4. Final Answer:

   arr2 = np.array([[1, 0], [0, 1], [1, 1]]) -> Option C

5. Quick Check:

   Matrix shapes must align for dot product [OK]

Hint: Check matrix shapes before multiplying [OK]

Common Mistakes:

• Ignoring shape mismatch in dot product
• Confusing rows and columns after transpose
• Choosing arrays with incompatible shapes