Element-wise operations (.*, ./, .^) in MATLAB - Mini Project: Build & Apply

Element-wise Operations in MATLAB

📖 Scenario: Imagine you have two lists of numbers representing daily sales and daily costs for a small shop. You want to calculate the profit for each day by subtracting costs from sales, then find the profit margin by dividing profit by sales, and finally calculate the profit growth by squaring the profit values.

🎯 Goal: You will create two vectors for sales and costs, then use element-wise operations .*, ./, and .^ to calculate profit, profit margin, and profit growth for each day.

📋 What You'll Learn

Create two vectors called sales and costs with exact values

Create a variable called days to store the number of days

Calculate profit using element-wise subtraction

Calculate profit_margin using element-wise division

Calculate profit_growth using element-wise power

Display the results using disp

💡 Why This Matters

🌍 Real World

Element-wise operations are useful when you want to perform calculations on each item in a list or array separately, like calculating daily profits or growth rates.

💼 Career

Understanding element-wise operations is important for data analysis, financial modeling, and scientific computing where you work with arrays of data.

1

Create sales and costs vectors

Create a row vector called sales with values [100, 150, 200, 250, 300] and a row vector called costs with values [60, 90, 120, 160, 180].

MATLAB

% Create vectors sales and costs
% Your code here

Hint

Use square brackets [] to create row vectors with commas separating the numbers.

2

Create days variable

Create a variable called days that stores the number of elements in the sales vector using the length function.

MATLAB

sales = [100, 150, 200, 250, 300];
costs = [60, 90, 120, 160, 180];
% Create variable days to store length of sales
% Your code here

Hint

Use length(sales) to find how many numbers are in the sales vector.

3

Calculate profit, profit margin, and profit growth

Calculate profit by subtracting costs from sales using element-wise subtraction. Then calculate profit_margin by dividing profit by sales using element-wise division. Finally, calculate profit_growth by squaring each element of profit using element-wise power.

MATLAB

sales = [100, 150, 200, 250, 300];
costs = [60, 90, 120, 160, 180];
days = length(sales);
% Calculate profit, profit_margin, and profit_growth
% Your code here

Hint

Use - for subtraction, ./ for element-wise division, and .^ for element-wise power.

4

Display the results

Use disp to display the variables profit, profit_margin, and profit_growth.

MATLAB

sales = [100, 150, 200, 250, 300];
costs = [60, 90, 120, 160, 180];
days = length(sales);
profit = sales - costs;
profit_margin = profit ./ sales;
profit_growth = profit .^ 2;
% Display profit, profit_margin, and profit_growth
% Your code here

Hint

Use disp('text') to show labels and disp(variable) to show values.

Practice

1. In MATLAB, what does the operator .* do when applied between two arrays of the same size?

easy

A. Performs matrix multiplication of the arrays

B. Performs element-wise multiplication of the arrays

C. Divides the first array by the second array element-wise

D. Raises each element of the first array to the power of the second array

Solution

1. Step 1: Understand the operator .* in MATLAB

   The .* operator multiplies corresponding elements of two arrays of the same size.

2. Step 2: Differentiate from matrix multiplication

   Matrix multiplication uses * without the dot and follows linear algebra rules, unlike element-wise multiplication.

3. Final Answer:

   Performs element-wise multiplication of the arrays -> Option B

4. Quick Check:

   .* means element-wise multiply [OK]

Hint: Dot before operator means element-wise operation [OK]

Common Mistakes:

• Confusing .* with matrix multiplication *
• Thinking .* divides arrays
• Assuming .* raises to power

2. Which of the following is the correct syntax for element-wise division of two arrays A and B in MATLAB?

easy

A. A / B

B. A .\ B

C. A ./ B

D. A // B

Solution

1. Step 1: Recall element-wise division syntax

   Element-wise division in MATLAB uses ./ between arrays.

2. Step 2: Identify incorrect options

   / is matrix right division, .\ is element-wise left division, and // is not valid in MATLAB.

3. Final Answer:

   A ./ B -> Option C

4. Quick Check:

   ./ means element-wise division [OK]

Hint: Use dot before slash for element-wise division [OK]

Common Mistakes:

• Using / instead of ./
• Confusing left and right division operators
• Using invalid operators like //

3. What is the output of the following MATLAB code?

A = [2, 4; 6, 8];
B = [1, 2; 3, 4];
C = A .^ B;

medium

A. [2, 16; 216, 4096]

B. [2, 8; 18, 32]

C. [2, 4; 6, 8]

D. Error due to incompatible sizes

Solution

1. Step 1: Understand element-wise power operation

   The operator .^ raises each element of A to the power of the corresponding element in B.

2. Step 2: Calculate each element

   Calculations:
   2^1 = 2
   4^2 = 16
   6^3 = 216
   8^4 = 4096

3. Final Answer:

   [2, 16; 216, 4096] -> Option A

4. Quick Check:

   Element-wise power = calculated matrix [OK]

Hint: Use .^ to power elements individually [OK]

Common Mistakes:

• Confusing .^ with matrix power ^
• Calculating powers incorrectly
• Assuming size mismatch error

4. Consider this MATLAB code snippet:

X = [1, 2, 3];
Y = [4, 5];
Z = X .* Y;

What is the issue with this code?

medium

A. Syntax error due to missing semicolon

B. Code runs correctly and returns [4, 10, 15]

C. Z will be a scalar value

D. Dimension mismatch error for element-wise multiplication

Solution

1. Step 1: Check array sizes for element-wise multiplication

   X is 1x3 and Y is 1x2, sizes do not match.

2. Step 2: Understand MATLAB behavior on size mismatch

   Element-wise operations require arrays of the same size or compatible broadcasting, which MATLAB does not support here.

3. Final Answer:

   Dimension mismatch error for element-wise multiplication -> Option D

4. Quick Check:

   Different sizes cause error in .* [OK]

Hint: Arrays must be same size for element-wise ops [OK]

Common Mistakes:

• Assuming MATLAB auto-broadcasts arrays
• Ignoring size mismatch errors
• Thinking semicolon affects operation

5. You have two matrices in MATLAB:

M = [1, 2, 3; 4, 5, 6];
N = [2, 0, 1; 3, 4, 5];

You want to create a new matrix R where each element is the result of M element-wise multiplied by N, then divided element-wise by N plus 1. Which MATLAB expression correctly computes R?

hard

A. R = (M .* N) ./ (N + 1);

B. R = M * N ./ (N + 1);

C. R = M .* (N ./ (N + 1));

D. R = (M .* N) / (N + 1);

Solution

1. Step 1: Identify element-wise multiplication and division

   Element-wise multiplication uses .* and element-wise division uses ./.

2. Step 2: Analyze each option

   R = (M .* N) ./ (N + 1); correctly uses .* and ./ with parentheses.
   R = M * N ./ (N + 1); uses matrix multiplication *, which is incorrect.
   R = M .* (N ./ (N + 1)); changes the order of operations, not matching the problem.
   R = (M .* N) / (N + 1); uses matrix division /, which is invalid here.

3. Final Answer:

   R = (M .* N) ./ (N + 1); -> Option A

4. Quick Check:

   Use dot operators for element-wise multiply and divide [OK]

Hint: Use parentheses and dot operators for element-wise math [OK]

Common Mistakes:

• Using matrix multiplication instead of element-wise
• Forgetting dot before division operator
• Misplacing parentheses changing operation order