Element-wise operations (.*, ./, .^) in MATLAB - Cheat Sheet & Quick Revision

Recall & Review

beginner

What does the operator .* do in MATLAB?

The .* operator performs element-wise multiplication between two arrays of the same size. It multiplies each element in one array by the corresponding element in the other array.

beginner

How is element-wise division represented in MATLAB?

Element-wise division is done using the ./ operator. It divides each element of the first array by the corresponding element of the second array.

intermediate

Explain the difference between * and .* in MATLAB.

* is matrix multiplication, which follows linear algebra rules. .* multiplies arrays element by element, requiring arrays to be the same size or compatible for broadcasting.

beginner

What does the operator .^ do in MATLAB?

The .^ operator raises each element of an array to the power of the corresponding element in another array, performing element-wise exponentiation.

beginner

Why must arrays be the same size for element-wise operations in MATLAB?

Because element-wise operations work by pairing elements at the same positions, arrays must have matching sizes so each element has a partner to operate with.

Which operator performs element-wise multiplication in MATLAB?

A .*

B *

C ./

D .^

The operator .* multiplies arrays element by element.

What happens if you try to use .* on arrays of different sizes?

A MATLAB automatically resizes arrays

B MATLAB returns an error

C MATLAB performs matrix multiplication

D MATLAB ignores extra elements

Element-wise operations require arrays to be the same size; otherwise, MATLAB throws an error.

Which operator would you use to raise each element of an array to the power of 2?

A ^2

B *2

C .^2

D .*2

The .^ operator performs element-wise exponentiation.

What does the operator ./ do?

A Matrix multiplication

B Matrix division

C Element-wise multiplication

D Element-wise division

./ divides each element of one array by the corresponding element of another.

Which operator is used for matrix multiplication in MATLAB?

A *

B .*

C ./

D .^

The * operator performs matrix multiplication following linear algebra rules.

Describe how element-wise multiplication differs from matrix multiplication in MATLAB.

Think about how each element is paired in both operations.

Explain why element-wise operators in MATLAB start with a dot (e.g., .*, ./, .^).

Consider how MATLAB differentiates between matrix and element-wise operations.

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