Element-wise operations (.*, ./, .^) in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of element-wise multiplication

What is the output of the following MATLAB code?

MATLAB

A = [1 2 3];
B = [4 5 6];
C = A .* B;
disp(C);

A [4 10 18]

B [5 7 9]

C [4 5 6]

D [1 2 3 4 5 6]

💡 Hint

Remember that .* multiplies each element of A by the corresponding element of B.

The operator .* performs element-wise multiplication. So each element in A is multiplied by the corresponding element in B: 1*4=4, 2*5=10, 3*6=18.

❓ Predict Output

intermediate

Result of element-wise division

What will be displayed after running this MATLAB code?

MATLAB

X = [10 20 30];
Y = [2 4 5];
Z = X ./ Y;
disp(Z);

A [5 5 6.0000]

B [5 4 6]

C [5 5 6]

D [5 5 6.0]

💡 Hint

Element-wise division divides each element of X by the corresponding element of Y.

The operator ./ divides each element of X by the corresponding element of Y: 10/2=5, 20/4=5, 30/5=6.

❓ Predict Output

advanced

Output of element-wise power operation

What is the output of this MATLAB code snippet?

MATLAB

P = [2 3 4];
Q = [3 2 1];
R = P .^ Q;
disp(R);

A [6 5 4]

B [8 9 1]

C [8 6 4]

D [8 9 4]

💡 Hint

The .^ operator raises each element of P to the power of the corresponding element in Q.

Element-wise power means: 2^3=8, 3^2=9, 4^1=4. So the result is [8 9 4].

❓ Predict Output

advanced

Error type from wrong operator usage

What error does this MATLAB code produce?

MATLAB

A = [1 2 3];
B = [4 5 6];
C = A * B;

A Error: Undefined operator '*' for input arguments of type 'double'.

B Error: Inner matrix dimensions must agree.

C No error, output is [4 10 18].

D Error: Matrix dimensions must agree for element-wise multiplication.

💡 Hint

The * operator is matrix multiplication and requires matching inner dimensions.

A is 1x3 and B is 1x3, so their inner dimensions (3 and 1) do not match for matrix multiplication. MATLAB throws an error about inner matrix dimensions.

🧠 Conceptual

expert

Number of elements in result after element-wise operations

Given two matrices A (2x3) and B (2x3), what is the number of elements in the result of A .* B?

A 6

B 2

C 3

D 1

💡 Hint

Element-wise operations keep the same size as the input matrices.

Element-wise multiplication produces a matrix of the same size as the inputs. Since A and B are 2 rows by 3 columns, the result has 2*3=6 elements.

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