Types of matrices - Question Bank
1. The identity matrix of order 2x2 is denoted by:
2. A matrix A is called Hermitian if A^θ = A. For a real matrix to be Hermitian, it must be:
3. A matrix A is called skew-Hermitian if A^θ = -A, where A^θ is the conjugate transpose of A. For a real matrix to be skew-Hermitian, it must be:
4. If A = [[1, 0], [2, 3]], this is an example of a:
5. If A = [[1, 2], [0, 3]], this is an example of a:
6. If A = [[1, 2], [3, 4]], this is an example of a:
7. If A = [[0, 0], [0, 0]], this is an example of a:
8. If A = [[1, 0], [0, 1]], this is an example of a:
9. If A = [[5, 0], [0, 5]], this is an example of a:
10. If A = [[2, 0], [0, 3]], this is an example of a:
11. A square matrix A is called nilpotent of index k if A^k = 0 and A^(k-1) ≠ 0. If k=1, then A is:
12. Which type of matrix is both upper triangular and lower triangular?
13. A matrix of order 1x1 is always a:
14. A matrix where at least one element is non-zero is called a:
15. A matrix where all the elements are negative is called a:
16. A matrix where all the elements are positive is called a:
17. A matrix A is involutory if A² = I. Which of the following is an involutory matrix?
18. A matrix A is idempotent if A² = A. Which of the following is an idempotent matrix?
19. A square matrix A is called periodic if A^k = I for some positive integer k. If k=1, then A is:
20. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The skew-symmetric part is given by:
21. Any matrix A can be expressed as the sum of a symmetric and a skew-symmetric matrix. The symmetric part is given by:
22. A matrix that becomes its negative after transposition is:
23. A matrix that remains unchanged after transposition is:
24. What is the order of a null matrix if it is also a square matrix?
25. If A is an orthogonal matrix, then A⁻¹ is equal to:
26. A matrix A is orthogonal if:
27. Which type of matrix has all diagonal elements equal and all non-diagonal elements zero?
28. A matrix where all elements are equal is called a:
29. A matrix of order m x n is rectangular if:
30. Which of the following is NOT a type of square matrix?
31. If A is a symmetric matrix, then A^T = ?
32. For a symmetric matrix A, the elements satisfy the condition:
33. A square matrix is called symmetric if its transpose is equal to:
34. If A is a skew-symmetric matrix, then A^T = ?
35. For a skew-symmetric matrix A, the diagonal elements must be:
36. A square matrix is called skew-symmetric if its transpose is equal to:
37. A triangular matrix is also a diagonal matrix if:
38. In a lower triangular matrix, the elements a_ij are zero when:
39. A matrix where all the elements above the main diagonal are zero is a:
40. In an upper triangular matrix, the elements a_ij are zero when:
41. A matrix where all the elements below the main diagonal are zero is a:
42. An identity matrix is always a:
43. A scalar matrix where the diagonal elements are all 1 is called a:
44. A square matrix where all the elements are identical and non-zero is a:
45. In a diagonal matrix, the elements a_ij are zero when:
46. A square matrix where all the non-diagonal elements are zero is termed as a:
47. A matrix with only one column is called a:
48. Which type of matrix has only one row?
49. A matrix where the number of rows is equal to the number of columns is known as a:
50. A matrix in which all the elements are zero is called a: