Matrix multiplication with @ operator in NumPy - Mini Project: Build & Apply

Matrix multiplication with @ operator

📖 Scenario: Imagine you work in a small company that analyzes sales data. You have two tables of numbers: one shows sales by product and month, and the other shows the price of each product. You want to find the total sales revenue for each month by multiplying these tables.

🎯 Goal: You will create two matrices using numpy, then multiply them using the @ operator to find total sales revenue per month.

📋 What You'll Learn

Create two numpy arrays with exact values

Use a variable to store the result of matrix multiplication

Use the @ operator for matrix multiplication

Print the resulting matrix

💡 Why This Matters

🌍 Real World

Matrix multiplication is used in many fields like sales analysis, computer graphics, and machine learning to combine data efficiently.

💼 Career

Knowing how to multiply matrices with numpy is a key skill for data scientists and analysts working with numerical data.

1

Create sales and price matrices

Import numpy as np. Create a numpy array called sales with these exact values: [[10, 20, 30], [5, 10, 25]]. Create another numpy array called prices with these exact values: [[2], [3], [4]].

NumPy

# Your code here

Hint

Use np.array() to create matrices with the exact numbers given.

2

Create a variable for total revenue

Create a variable called total_revenue and set it to None as a placeholder.

NumPy

import numpy as np
sales = np.array([[10, 20, 30], [5, 10, 25]])
prices = np.array([[2], [3], [4]])
# Your code here

Hint

Just create the variable total_revenue and assign None for now.

3

Multiply matrices using @ operator

Use the @ operator to multiply sales by prices. Store the result in the variable total_revenue.

NumPy

import numpy as np
sales = np.array([[10, 20, 30], [5, 10, 25]])
prices = np.array([[2], [3], [4]])
total_revenue = None
# Your code here

Hint

Use total_revenue = sales @ prices to multiply the matrices.

4

Print the total revenue matrix

Print the variable total_revenue to display the result of the matrix multiplication.

NumPy

import numpy as np
sales = np.array([[10, 20, 30], [5, 10, 25]])
prices = np.array([[2], [3], [4]])
total_revenue = sales @ prices
# Your code here

Hint

Use print(total_revenue) to show the final matrix.

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