Transpose & Symmetric Matrices

Grade 12 Maths — Transpose & Symmetric Matrices: 25 practice questions with instant scoring and explanations.

1. The transpose of a matrix A is denoted as:
2. If A is a 3 × 2 matrix, then A^T is:
3. If A = [[1, 2, 3], [4, 5, 6]], then A^T equals:
4. The property (A^T)^T = A means:
5. A symmetric matrix A satisfies:
6. Which of the following is a symmetric matrix?
7. A skew-symmetric matrix A satisfies:
8. If A is a skew-symmetric matrix, then its diagonal elements must be:
9. The property (AB)^T = B^T A^T is called:
10. If A = [[1, 2], [−2, 3]], then A is:
11. Any square matrix A can be written as:
12. The symmetric part of matrix A is:
13. The skew-symmetric part of matrix A is:
14. If A is symmetric, then A^T is:
15. If A is skew-symmetric, then A^T is:
16. An orthogonal matrix A satisfies:
17. If A is symmetric and B is symmetric, then AB is:
18. The trace of a symmetric matrix equals:
19. If A = [[2, 1], [1, 3]], then A is:
20. The property (kA)^T = k(A^T) for scalar k is:
21. If A is a skew-symmetric matrix of odd order, then det(A) equals:
22. A matrix that equals its own transpose is called:
23. If A = [[0, 2], [−2, 0]], then A is:
24. For any matrix A, the product AA^T is always:
25. Find f'(x) if f(x) = 3x²