MCQs on Matrix Manipulations | MATLAB

1. Advanced Matrix Operations (Transposition, Inversion)

1. What symbol is commonly used to denote the transpose of a matrix in MATLAB?
   • A. *
   • B. '
   • C. @
   • D. ^
2. Which function computes the inverse of a square matrix in MATLAB?
   • A. inv
   • B. transpose
   • C. eig
   • D. det
3. A matrix is invertible if and only if its determinant is:
   • A. Equal to zero
   • B. Greater than zero
   • C. Less than zero
   • D. Non-zero
4. The product of a matrix and its inverse is always:
   • A. A diagonal matrix
   • B. The identity matrix
   • C. A null matrix
   • D. Undefined
5. The transpose of a row vector is:
   • A. Another row vector
   • B. A column vector
   • C. A scalar
   • D. The original row vector
6. Which MATLAB function directly computes the Hermitian transpose of a matrix?
   • A. ctranspose
   • B. transpose
   • C. hermit
   • D. conjugate

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2. Linear Algebra (eig, inv, rank)

7. What does the eig function compute in MATLAB?
   • A. Eigenvalues and eigenvectors
   • B. Determinant
   • C. Rank of the matrix
   • D. Singular values
8. If a matrix has full rank, it implies:
   • A. The matrix is singular
   • B. The matrix is invertible
   • C. The determinant is zero
   • D. The matrix is not square
9. The rank of a matrix is defined as:
   • A. The number of rows
   • B. The number of non-zero rows in its reduced form
   • C. The determinant of the matrix
   • D. The number of columns
10. Which MATLAB function calculates the determinant of a matrix?
    • A. eig
    • B. det
    • C. rank
    • D. inv
11. What condition must be satisfied for eigenvalues to exist?
    • A. The matrix must be diagonal
    • B. The matrix must be square
    • C. The determinant must be zero
    • D. The rank must be full
12. Which command finds the pseudo-inverse of a matrix?
    • A. inv
    • B. pinv
    • C. eig
    • D. rank

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3. Sparse Matrices

13. Sparse matrices are advantageous because they:
    • A. Store all elements explicitly
    • B. Minimize memory usage by storing only non-zero elements
    • C. Increase computational time
    • D. Cannot be used for linear algebra operations
14. The function sparse in MATLAB:
    • A. Converts a matrix to full storage
    • B. Converts a matrix to sparse storage
    • C. Computes eigenvalues for sparse matrices
    • D. Finds the determinant of sparse matrices
15. Which of the following is a valid MATLAB function for sparse matrices?
    • A. nnz
    • B. spconvert
    • C. spy
    • D. All of the above
16. The nnz function returns:
    • A. The total number of elements in a matrix
    • B. The number of non-zero elements in a matrix
    • C. The determinant of the matrix
    • D. The eigenvalues of the matrix
17. To visualize the pattern of non-zero elements in a sparse matrix, you use:
    • A. spy
    • B. nnz
    • C. imshow
    • D. plot
18. Which function converts a sparse matrix to its full representation?
    • A. sparse
    • B. full
    • C. reshape
    • D. inv

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4. Reshaping and Sorting

19. What does the reshape function do in MATLAB?
    • A. Changes the data type of elements
    • B. Changes the size of a matrix without changing data order
    • C. Sorts the elements of a matrix
    • D. Computes eigenvalues
20. Which MATLAB function sorts the elements of a matrix?
    • A. sort
    • B. rank
    • C. reshape
    • D. eig
21. The sortrows function:
    • A. Sorts the matrix column-wise
    • B. Sorts the matrix row-wise
    • C. Sorts rows based on column values
    • D. Reshapes the matrix
22. To flatten a matrix into a single column, you use:
    • A. reshape(A, [], 1)
    • B. flatten(A)
    • C. sort(A)
    • D. compress(A)
23. Reshaping a matrix requires:
    • A. The product of the dimensions to remain constant
    • B. The matrix to be square
    • C. The determinant to be non-zero
    • D. The matrix to have integer elements
24. Sorting elements in descending order requires which syntax?
    • A. sort(A, 'ascend')
    • B. sort(A, 'descend')
    • C. sort(A, -1)
    • D. sort(A, 'rev')
25. Which MATLAB function rearranges a matrix based on a specified condition?
    • A. filter
    • B. sortrows
    • C. sort
    • D. reshape
26. The permute function is used for:
    • A. Rotating a matrix
    • B. Rearranging the dimensions of a matrix
    • C. Flattening a matrix
    • D. Sorting a matrix
27. To obtain unique elements of a matrix in sorted order, you use:
    • A. sort
    • B. unique
    • C. reshape
    • D. permute
28. Which function repeats a matrix along specified dimensions?
    • A. repmat
    • B. repeat
    • C. duplicate
    • D. expand
29. A vectorized operation on a matrix:
    • A. Reduces computational efficiency
    • B. Applies operations element-wise without loops
    • C. Only works with square matrices
    • D. Requires explicit storage of zeros
30. The flip function in MATLAB is used to:
    • A. Sort a matrix
    • B. Invert a matrix
    • C. Reverse the order of elements along a dimension
    • D. Compute the determinant

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Answers Table

Qno	Answer (Option with Text)
1	B. '
2	A. inv
3	D. Non-zero
4	B. The identity matrix
5	B. A column vector
6	A. ctranspose
7	A. Eigenvalues and eigenvectors
8	B. The matrix is invertible
9	B. The number of non-zero rows in its reduced form
10	B. det
11	B. The matrix must be square
12	B. pinv
13	B. Minimize memory usage by storing only non-zero elements
14	B. Converts a matrix to sparse storage
15	D. All of the above
16	B. The number of non-zero elements in a matrix
17	A. spy
18	B. full
19	B. Changes the size of a matrix without changing data order
20	A. sort
21	C. Sorts rows based on column values
22	A. reshape(A, [], 1)
23	A. The product of the dimensions to remain constant
24	B. sort(A, 'descend')
25	B. sortrows
26	B. Rearranging the dimensions of a matrix
27	B. unique
28	A. repmat
29	B. Applies operations element-wise without loops
30	C. Reverse the order of elements along a dimension