np.eye() for identity matrices in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a 3x3 identity matrix using numpy.

NumPy

import numpy as np
matrix = np.[1](3)
print(matrix)

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

Aones

Beye

Czeros

Darray

Attempts:

3 left

💡 Hint

Common Mistakes

Using np.ones() or np.zeros() instead of np.eye()

Forgetting to import numpy as np

The np.eye() function creates an identity matrix of given size.

2fill in blank

medium

Complete the code to create a 4x4 identity matrix with float type values.

NumPy

import numpy as np
matrix = np.eye(4, dtype=[1])
print(matrix)

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Afloat

Bint

Cstr

Dbool

Attempts:

3 left

💡 Hint

Common Mistakes

Using integer type which will show 1 and 0 without decimals

Using string or boolean types which are not suitable here

The dtype parameter sets the data type of the matrix elements. For decimal numbers, use float.

3fill in blank

hard

Fix the error in the code to create a 5x5 identity matrix with numpy.

NumPy

import numpy as np
matrix = np.eye([1])
print(matrix)

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A5

Bfive

C'5'

Dnp

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the size as a string instead of an integer

Passing a variable name that is not defined

The size parameter must be an integer without quotes. Using quotes makes it a string, causing an error.

4fill in blank

hard

Fill both blanks to create a 3x5 identity-like matrix with ones on the diagonal.

NumPy

import numpy as np
matrix = np.eye([1], [2])
print(matrix)

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A3

B4

C5

D6

Attempts:

3 left

💡 Hint

Common Mistakes

Swapping rows and columns

Using equal numbers for both parameters

The first parameter is the number of rows (3), the second is the number of columns (5) for a rectangular identity matrix.

5fill in blank

hard

Fill all three blanks to create a 4x4 identity matrix with ones on the diagonal shifted by 1 above the main diagonal.

NumPy

import numpy as np
matrix = np.eye([1], [2], k=[3])
print(matrix)

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

A4

C1

D-1

Attempts:

3 left

💡 Hint

Common Mistakes

Using negative k which shifts below the main diagonal

Using different sizes for rows and columns

The first two parameters set the size (4x4). The k=1 shifts the diagonal of ones one position above the main diagonal.

Practice

1. What does the function np.eye(4) create in NumPy?

easy

A. A 4x4 identity matrix with 1s on the main diagonal

B. A 4x4 matrix filled with zeros

C. A 4x4 matrix filled with ones

D. A 4x4 diagonal matrix with 1s on the first upper diagonal

Solution

1. Step 1: Understand np.eye() default behavior

   By default, np.eye(n) creates an n x n identity matrix with 1s on the main diagonal and 0s elsewhere.

2. Step 2: Apply np.eye(4)

   Calling np.eye(4) creates a 4x4 matrix with 1s on the main diagonal and 0s elsewhere.

3. Final Answer:

   A 4x4 identity matrix with 1s on the main diagonal -> Option A

4. Quick Check:

   np.eye(4) = 4x4 identity matrix [OK]

Hint: np.eye(n) makes nxn identity matrix by default [OK]

Common Mistakes:

• Confusing np.eye() with np.ones() or np.zeros()
• Thinking np.eye() fills all elements with 1
• Assuming 1s are on an off-diagonal by default

2. Which of the following is the correct syntax to create a 3x5 identity matrix with 1s on the main diagonal using np.eye()?

easy

A. np.eye(5, 3)

B. np.eye(3, 5)

C. np.eye(3)

D. np.eye(5)

Solution

1. Step 1: Understand np.eye() parameters

   The first parameter is the number of rows, the second is columns. So np.eye(3, 5) creates a 3x5 matrix.

2. Step 2: Check the options

   np.eye(3, 5) correctly uses np.eye(3, 5) to create a 3x5 matrix with 1s on the main diagonal.

3. Final Answer:

   np.eye(3, 5) -> Option B

4. Quick Check:

   np.eye(rows, cols) = correct syntax [OK]

Hint: First arg = rows, second = columns in np.eye() [OK]

Common Mistakes:

• Swapping rows and columns parameters
• Using only one parameter for non-square matrix
• Confusing np.eye() with np.identity()

3. What is the output of the following code?

import numpy as np
print(np.eye(3, k=1))

medium

A. [[0. 0. 1.]
[0. 1. 0.]
[1. 0. 0.]]

B. [[1. 0. 0.]
[0. 1. 0.]
[0. 0. 1.]]

C. [[0. 0. 0.]
[1. 0. 0.]
[0. 1. 0.]]

D. [[0. 1. 0.]
[0. 0. 1.]
[0. 0. 0.]]

Solution

1. Step 1: Understand the k parameter in np.eye()

   The parameter k=1 shifts the diagonal of 1s one above the main diagonal.

2. Step 2: Visualize the 3x3 matrix with 1s on the first upper diagonal

   The 1s appear at positions (0,1) and (1,2), zeros elsewhere.

3. Final Answer:

   [[0. 1. 0.] [0. 0. 1.] [0. 0. 0.]] -> Option D

4. Quick Check:

   k=1 shifts diagonal up by 1 [OK]

Hint: k shifts diagonal: 0=main, 1=above, -1=below [OK]

Common Mistakes:

• Ignoring the k parameter effect
• Assuming k=1 means main diagonal
• Confusing rows and columns in output

4. The code below throws an error. What is the mistake?

import numpy as np
matrix = np.eye(4, 3, k=4)
print(matrix)

medium

A. np.eye() does not accept three arguments

B. The matrix must be square for np.eye()

C. The value of k is too large for the matrix shape

D. The print statement is incorrect

Solution

1. Step 1: Check the meaning of k relative to matrix size

   The parameter k=4 means the diagonal of 1s is shifted 4 above the main diagonal.

2. Step 2: Compare k with matrix dimensions

   For a 4x3 matrix, the maximum upper diagonal shift is 2 (columns - 1). k=4 is invalid and causes an error.

3. Final Answer:

   The value of k is too large for the matrix shape -> Option C

4. Quick Check:

   k must be within valid diagonal range [OK]

Hint: k must fit within matrix diagonal limits [OK]

Common Mistakes:

• Assuming any k value works
• Thinking np.eye() only creates square matrices
• Blaming print instead of parameter error

5. You want to create a 5x5 matrix with 1s on the diagonal just below the main diagonal using np.eye(). Which code achieves this and what is the resulting matrix?

hard

A. np.eye(5, k=-1) resulting in 1s at positions (1,0), (2,1), (3,2), (4,3)

B. np.eye(5, k=1) resulting in 1s at positions (0,1), (1,2), (2,3), (3,4)

C. np.eye(5) resulting in 1s on the main diagonal

D. np.eye(5, k=-2) resulting in 1s two diagonals below the main

Solution

1. Step 1: Understand k parameter for diagonal shift

   Negative k shifts the diagonal of 1s below the main diagonal. k=-1 means one diagonal below.

2. Step 2: Apply np.eye(5, k=-1)

   This creates a 5x5 matrix with 1s at positions (1,0), (2,1), (3,2), (4,3) and zeros elsewhere.

3. Final Answer:

   np.eye(5, k=-1) with 1s just below main diagonal -> Option A

4. Quick Check:

   k=-1 shifts diagonal down by 1 [OK]

Hint: Use negative k for diagonals below main [OK]

Common Mistakes:

• Using positive k for below main diagonal
• Confusing positions of 1s in matrix
• Assuming np.eye() only creates main diagonal