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.