Matrix transpose in MATLAB - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

What is the output of this matrix transpose code?

Consider the following MATLAB code that transposes a matrix. What will be the output?

MATLAB

A = [1 2 3; 4 5 6];
B = A';
disp(B);

A [1 4 3; 2 5 6]

B [1 2 3; 4 5 6]

C [1 4 2; 5 3 6]

D [1 4; 2 5; 3 6]

💡 Hint

Remember that the transpose flips rows and columns.

The transpose operator (') swaps rows and columns. The original matrix A has 2 rows and 3 columns, so B will have 3 rows and 2 columns with elements flipped accordingly.

🧠 Conceptual

intermediate

What does the transpose operator (') do to a matrix?

In MATLAB, what is the effect of applying the transpose operator (') to a matrix?

A It rotates the matrix 90 degrees clockwise.

B It reverses the order of elements in each row.

C It flips the matrix over its main diagonal, swapping rows and columns.

D It replaces all elements with their negatives.

💡 Hint

Think about how rows and columns change positions.

The transpose operator swaps the rows and columns of the matrix, effectively flipping it over its main diagonal.

🔧 Debug

advanced

What happens when transposing a cell array with ' operator?

What happens if you try to transpose a cell array using the ' operator in MATLAB?

MATLAB

C = {1, 2; 3, 4};
D = C';

A No error, D is the transposed cell array.

B Error: Cell arrays cannot be transposed using '. Use transpose() instead.

C Error: Invalid use of operator ' for cell arrays.

D Error: Undefined function or variable 'C'.

💡 Hint

Check MATLAB documentation for transposing cell arrays.

No error occurs. The ' operator transposes cell arrays by swapping rows and columns, just like for numeric matrices. For this C, D = {1, 3; 2, 4}.

❓ Predict Output

advanced

What is the output of transposing a complex matrix with ' operator?

Given the matrix with complex numbers, what is the output of the transpose operation?

MATLAB

M = [1+1i, 2-1i; 3+0i, 4+4i];
T = M';
disp(T);

A [1-1i 3-0i; 2+1i 4-4i]

B [1+1i 3+0i; 2-1i 4+4i]

C [1+1i 2-1i; 3+0i 4+4i]

D [1-1i 2+1i; 3-0i 4-4i]

💡 Hint

The ' operator does conjugate transpose for complex matrices.

In MATLAB, the ' operator performs conjugate transpose, which flips the matrix and takes the complex conjugate of each element.

❓ Predict Output

expert

What is the output of transposing a sparse matrix?

Consider this sparse matrix and its transpose. What is the output of the following code?

MATLAB

S = sparse([1 3 4], [2 1 3], [10 20 30], 4, 4);
ST = S';
full(ST)

A [0 10 0 0; 20 0 0 0; 0 0 30 0; 0 0 0 0]

B [0 20 0 0; 10 0 0 0; 0 0 30 0; 0 0 0 0]

C [0 0 20 0; 10 0 0 0; 0 0 0 30; 0 0 0 0]

D [0 0 0 0; 10 0 0 0; 0 20 0 0; 0 0 30 0]

💡 Hint

Transpose swaps row and column indices in sparse matrices.

Transposing a sparse matrix swaps the row and column indices of nonzero elements. Using full() converts it to a full matrix for display.

Practice

1. What does the transpose operation do to a matrix in MATLAB?

easy

A. It swaps the rows and columns of the matrix.

B. It multiplies all elements by -1.

C. It adds a new row to the matrix.

D. It deletes the last column of the matrix.

Solution

1. Step 1: Understand matrix structure

   A matrix has rows and columns arranged in a grid.

2. Step 2: Define transpose operation

   Transposing swaps each row with the corresponding column, flipping the matrix over its diagonal.

3. Final Answer:

   It swaps the rows and columns of the matrix. -> Option A

4. Quick Check:

   Transpose = swap rows and columns [OK]

Hint: Transpose flips rows and columns in a matrix [OK]

Common Mistakes:

• Thinking transpose multiplies elements
• Confusing transpose with adding rows
• Assuming transpose deletes columns

2. Which of the following is the correct MATLAB syntax to transpose a matrix A?

easy

A. A.T

B. trans(A)

C. A'

D. A^T

Solution

1. Step 1: Recall MATLAB transpose operators

   In MATLAB, the apostrophe ' is used to transpose a matrix.

2. Step 2: Common incorrect syntax

   A.T is Python syntax; trans(A) and A^T are invalid in MATLAB.

3. Final Answer:

   A' -> Option C

4. Quick Check:

   Use apostrophe (') for transpose [OK]

Hint: Use apostrophe (') to transpose matrix in MATLAB [OK]

Common Mistakes:

• Using A^T which is invalid syntax
• Using A.T (Python syntax)
• Using trans(A) which is undefined

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

A = [1 2; 3 4];
B = A';
disp(B);

medium

A. [1 3; 2 4]

B. [1 2; 3 4]

C. [1 3; 4 2]

D. [2 1; 4 3]

Solution

1. Step 1: Understand matrix A

   Matrix A is 2x2: first row [1 2], second row [3 4].

2. Step 2: Apply transpose operation

   Transposing swaps rows and columns: first column becomes first row, second column becomes second row. So B = [1 3; 2 4].

3. Final Answer:

   [1 3; 2 4] -> Option A

4. Quick Check:

   Transpose swaps rows and columns [OK]

Hint: Swap rows and columns to find transpose [OK]

Common Mistakes:

• Mixing rows and columns incorrectly
• Confusing transpose with element-wise operations
• Reading matrix elements in wrong order

4. Identify the error in this MATLAB code snippet:

A = [1 2 3; 4 5 6];
B = A';
C = B(1,3);

medium

A. No error; code runs correctly.

B. Indexing error: B(1,3) is out of bounds after transpose.

C. Matrix A is not defined properly.

D. Syntax error: transpose operator used incorrectly.

Solution

1. Step 1: Analyze matrix A size

   A is 2 rows by 3 columns.

2. Step 2: Transpose matrix A

   After transpose, B is 3 rows by 2 columns.

3. Step 3: Check indexing B(1,3)

   Since B has only 2 columns, B(1,3) is out of bounds and will cause an error.

4. Final Answer:

   Indexing error: B(1,3) is out of bounds after transpose. -> Option B

5. Quick Check:

   Check matrix size before indexing [OK]

Hint: Check matrix size after transpose before indexing [OK]

Common Mistakes:

• Assuming size stays same after transpose
• Ignoring column count when indexing
• Confusing row and column indices

5. Given a complex matrix C = [1+2i, 3-4i; 5+6i, 7-8i], which MATLAB expression returns the transpose without conjugation?

hard

A. C'

B. C.T

C. ctranspose(C)

D. C.'

Solution

1. Step 1: Understand transpose with complex numbers

   In MATLAB, C' transposes and conjugates complex matrices.

2. Step 2: Identify transpose without conjugation

   The operator .' transposes without conjugating complex elements.

3. Step 3: Check other options

   ctranspose(C) performs conjugate transpose; C.T is invalid syntax.

4. Final Answer:

   C.' -> Option D

5. Quick Check:

   Use dot-apostrophe (.' ) for transpose without conjugation [OK]

Hint: Use dot-apostrophe (.' ) to transpose without conjugation [OK]

Common Mistakes:

• Using apostrophe (') which conjugates
• Confusing transpose and conjugate
• Using ctranspose(C) which conjugates