np.dot() for dot product in NumPy - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of np.dot() with 1D arrays

What is the output of this code using np.dot() on two 1D arrays?

NumPy

import numpy as np

x = np.array([1, 2, 3])
y = np.array([4, 5, 6])
result = np.dot(x, y)
print(result)

A TypeError

B [4 10 18]

C 32

D [24 30 36]

💡 Hint

Recall that np.dot() between two 1D arrays calculates the sum of products of corresponding elements.

The dot product of two 1D arrays is the sum of the products of their elements: (1*4) + (2*5) + (3*6) = 4 + 10 + 18 = 32.

❓ Predict Output

intermediate

np.dot() with 2D arrays (matrix multiplication)

What is the output of this code using np.dot() on two 2D arrays?

NumPy

import numpy as np

A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
result = np.dot(A, B)
print(result)

A ValueError

B

[[12 16]
 [28 40]]

C

[[5 12]
 [21 32]]

D

[[19 22]
 [43 50]]

💡 Hint

Remember that np.dot() on 2D arrays performs matrix multiplication.

Matrix multiplication result is calculated as:
First row, first column: 1*5 + 2*7 = 19
First row, second column: 1*6 + 2*8 = 22
Second row, first column: 3*5 + 4*7 = 43
Second row, second column: 3*6 + 4*8 = 50

❓ data_output

advanced

Shape of np.dot() result with mixed dimensions

Given these arrays, what is the shape of the result from np.dot(A, B)?

NumPy

import numpy as np

A = np.array([[1, 2, 3], [4, 5, 6]])  # shape (2, 3)
B = np.array([7, 8, 9])                # shape (3,)
result = np.dot(A, B)
print(result.shape)

A (3,)

B (2,)

C (2, 3)

D ValueError

💡 Hint

When dot product involves a 2D array and a 1D array, the result shape depends on the 2D array's rows.

Dot product of (2,3) and (3,) arrays results in a 1D array with length 2, so shape is (2,).

🔧 Debug

advanced

Error raised by np.dot() with incompatible shapes

What error does this code raise when using np.dot() with incompatible shapes?

NumPy

import numpy as np

A = np.array([1, 2])  # shape (2,)
B = np.array([[3, 4], [5, 6], [7, 8]])  # shape (3, 2)
result = np.dot(A, B)
print(result)

A ValueError: shapes (2,) and (3,2) not aligned: 2 (dim 0) != 3 (dim 0)

B TypeError: unsupported operand type(s) for *: 'int' and 'list'

C IndexError: index out of bounds

D No error, output is [17 20]

💡 Hint

Check the dimensions of arrays to see if they can be multiplied.

np.dot() requires the inner dimensions to match. Here, (2,) and (3,2) do not align because 2 != 3.

🚀 Application

expert

Using np.dot() to compute cosine similarity

You want to compute the cosine similarity between two vectors a and b using np.dot(). Which option correctly computes it?

NumPy

import numpy as np

a = np.array([1, 2, 3])
b = np.array([4, 5, 6])

# Choose the correct formula for cosine similarity

A np.dot(a, b) / (np.linalg.norm(a) * np.linalg.norm(b))

B np.dot(a, b) * (np.linalg.norm(a) + np.linalg.norm(b))

C np.dot(a, b) / (np.linalg.norm(a) + np.linalg.norm(b))

D np.dot(a, b) - (np.linalg.norm(a) * np.linalg.norm(b))

💡 Hint

Cosine similarity is the dot product divided by the product of vector lengths.

Cosine similarity formula: (a · b) / (||a|| * ||b||), where ||a|| is the length (norm) of vector a.