Element-wise operations (.*, ./, .^) in MATLAB - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to multiply each element of vectors A and B element-wise.

MATLAB

C = A [1] B;

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

A.*

B./

C.+

D*

Attempts:

3 left

💡 Hint

Common Mistakes

Using * instead of .* causes matrix multiplication, which may error if dimensions mismatch.

In MATLAB, .* performs element-wise multiplication between arrays.

2fill in blank

medium

Complete the code to divide each element of vector X by corresponding element of Y element-wise.

MATLAB

Z = X [1] Y;

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

A.\

B/

C\

D./

Attempts:

3 left

💡 Hint

Common Mistakes

Using / performs matrix division, not element-wise division.

The ./ operator divides elements of arrays element-wise in MATLAB.

3fill in blank

hard

Fix the error in the code to raise each element of vector V to the power of 3 element-wise.

MATLAB

W = V [1] 3;

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

A^

B.*

C.^

D./

Attempts:

3 left

💡 Hint

Common Mistakes

Using ^ performs matrix power, which is not element-wise.

The .^ operator raises each element of an array to a power element-wise.

4fill in blank

hard

Fill both blanks to compute element-wise multiplication and then element-wise division of vectors A and B.

MATLAB

result = (A [1] B) [2] B;

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

A.*

B+

C./

D-

Attempts:

3 left

💡 Hint

Common Mistakes

Using + or - instead of element-wise multiplication or division.

First, use .* for element-wise multiplication, then ./ for element-wise division.

5fill in blank

hard

Fill all three blanks to compute element-wise power, then multiply element-wise, and finally divide element-wise.

MATLAB

output = ((X [1] 2) [2] Y) [3] Z;

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

A.^

B.*

C./

D+

Attempts:

3 left

💡 Hint

Common Mistakes

Using + instead of element-wise operators.

Mixing matrix operators with element-wise operators.

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

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