Matrix multiplication with @ operator in NumPy - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to multiply two matrices using the @ operator.

NumPy

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

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

A*

B+

C-

D@

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of @ for matrix multiplication.

Using + or - operators which perform addition or subtraction.

The @ operator performs matrix multiplication in numpy.

2fill in blank

medium

Complete the code to multiply matrix A by matrix B and store the result in variable C.

NumPy

import numpy as np
A = np.array([[2, 0], [1, 3]])
B = np.array([[1, 4], [2, 5]])
C = A [1] B
print(C)

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

A//

B**

C@

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * which multiplies elements individually.

Using // or ** which are not valid for matrix multiplication.

The @ operator correctly multiplies matrices A and B.

3fill in blank

hard

Fix the error in the code to correctly multiply matrices A and B.

NumPy

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([[7, 8], [9, 10], [11, 12]])
result = A [1] B
print(result)

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

A-

B@

C+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * which causes shape mismatch error.

Using + or - which are invalid for matrix multiplication.

The @ operator performs matrix multiplication correctly for these shapes.

4fill in blank

hard

Fill both blanks to create a matrix multiplication and print the shape of the result.

NumPy

import numpy as np
A = np.array([[1, 0], [0, 1]])
B = np.array([[4, 1], [2, 2]])
result = A [1] B
print(result[2])

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

A@

B*

C.shape

D.size

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of @ for multiplication.

Using .size instead of .shape to get dimensions.

Use @ for matrix multiplication and .shape to get the dimensions of the result.

5fill in blank

hard

Fill all three blanks to multiply matrices and extract the element at row 1, column 0 of the result.

NumPy

import numpy as np
A = np.array([[3, 5], [7, 9]])
B = np.array([[2, 4], [6, 8]])
result = A [1] B
value = result[2][3]
print(value)

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

A@

B[1, 0]

D[1][0]

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of @ for multiplication.

Using a single bracket with comma inside for indexing.

Use @ for matrix multiplication and [1][0] to access the element at row 1, column 0.

Practice

1. What does the @ operator do in numpy when applied between two arrays?

easy

A. Performs matrix multiplication if shapes are compatible

B. Adds the two arrays element-wise

C. Calculates the element-wise product

D. Computes the transpose of the first array

Solution

1. Step 1: Understand the @ operator purpose

   The @ operator in numpy is designed for matrix multiplication, which requires the inner dimensions of the two arrays to match.

2. Step 2: Differentiate from other operations

   Element-wise addition or multiplication use + or * respectively, not @. Transpose uses .T.

3. Final Answer:

   Performs matrix multiplication if shapes are compatible -> Option A

4. Quick Check:

   @ means matrix multiply [OK]

Hint: Remember: @ means matrix multiply, not element-wise [OK]

Common Mistakes:

• Confusing @ with element-wise multiplication
• Thinking @ adds arrays
• Assuming @ transposes arrays

2. Which of the following is the correct syntax to multiply two numpy arrays A and B using the @ operator?

easy

A. C = A * B

B. C = A + B

C. C = A.dot(B)

D. C = A @ B

Solution

1. Step 1: Identify the @ operator usage

   The @ operator is used as C = A @ B to perform matrix multiplication in numpy.

2. Step 2: Differentiate from other operations

   A * B is element-wise multiplication, A.dot(B) is a method but not using @, and A + B is addition.

3. Final Answer:

   C = A @ B -> Option D

4. Quick Check:

   Use @ between arrays for matrix multiply [OK]

Hint: Use @ directly between arrays for matrix multiply [OK]

Common Mistakes:

• Using * instead of @ for matrix multiply
• Confusing method dot() with operator @
• Using addition operator + mistakenly

3. What is the output of the following code?

import numpy as np
A = np.array([[1, 2], [3, 4]])
B = np.array([[5, 6], [7, 8]])
C = A @ B
print(C)

medium

A. [[ 5 12]
[21 32]]

B. [[ 6 8]
[10 12]]

C. [[19 22]
[43 50]]

D. [[ 5 6]
[ 7 8]]

Solution

1. Step 1: Calculate matrix multiplication manually

   Multiply rows of A by columns of B:
   First row: (1*5 + 2*7) = 19, (1*6 + 2*8) = 22
   Second row: (3*5 + 4*7) = 43, (3*6 + 4*8) = 50

2. Step 2: Confirm output matches calculation

   The resulting matrix is [[19, 22], [43, 50]], which matches [[19 22] [43 50]].

3. Final Answer:

   [[19 22] [43 50]] -> Option C

4. Quick Check:

   Matrix multiply result = [[19 22] [43 50]] [OK]

Hint: Multiply rows by columns and sum for each element [OK]

Common Mistakes:

• Adding elements instead of multiplying and summing
• Mixing element-wise multiplication with matrix multiplication
• Confusing row and column order

4. What error will occur when running this code?

import numpy as np
A = np.array([[1, 2, 3], [4, 5, 6]])
B = np.array([[7, 8], [9, 10]])
C = A @ B

medium

A. ValueError: shapes (2,3) and (2,2) not aligned for matrix multiplication

B. TypeError: unsupported operand type(s) for @

C. No error, output is a (2,2) matrix

D. IndexError: index out of bounds

Solution

1. Step 1: Check shapes of arrays

   Array A shape is (2,3), array B shape is (2,2). For matrix multiplication, A's columns (3) must equal B's rows (2).

2. Step 2: Identify mismatch and error

   Since 3 != 2, numpy raises a ValueError about shape misalignment.

3. Final Answer:

   ValueError: shapes (2,3) and (2,2) not aligned for matrix multiplication -> Option A

4. Quick Check:

   Matrix multiply needs matching inner dimensions [OK]

Hint: Check inner dimensions match before using @ [OK]

Common Mistakes:

• Ignoring shape mismatch and expecting output
• Confusing element-wise multiplication with matrix multiplication
• Assuming @ works like addition

5. Given two numpy arrays:

A = np.array([[1, 0], [0, 1]])
B = np.array([[2, 3], [4, 5]])

What is the result of C = A @ B @ A?

hard

A. [[5 8]
[9 14]]

B. [[2 3]
[4 5]]

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

D. [[2 4]
[3 5]]

Solution

1. Step 1: Multiply A and B

   Matrix A is the identity matrix. Multiplying identity with B returns B:
   A @ B = B = [[2, 3], [4, 5]]

2. Step 2: Multiply result by A again

   Multiplying B by identity matrix A again returns B:
   B @ A = B = [[2, 3], [4, 5]]

3. Final Answer:

   [[2 3] [4 5]] -> Option B

4. Quick Check:

   Identity matrix leaves other matrix unchanged [OK]

Hint: Identity matrix A leaves matrix unchanged when multiplied [OK]

Common Mistakes:

• Multiplying incorrectly and swapping rows/columns
• Assuming multiplication changes matrix when identity is involved
• Confusing element-wise and matrix multiplication