Matrix.
2. What is a column matrix?
3. What defines a square matrix?
4. What is a diagonal matrix?
5. What is a scalar matrix?
6. What defines a symmetric matrix?
7. What is a skew-symmetric matrix?
8. What is an identity matrix?
9. What defines an upper triangular matrix?
10. What defines a lower triangular matrix?
11. What is a singular matrix?
12. What is a non-singular matrix?
13. When are two matrices considered equal?
14. What is the result of adding two matrices A and B?
15. What is the result of subtracting matrix B from matrix A?
16. What is a negative matrix?
17. Which law states that \(A + B = B + A\) for matrices?
18. Which law states that \(A + (B + C) = (A + B) + C\) for matrices?
19. What is the additive identity matrix?
20. What is the additive inverse of matrix A?
21. What does the cancellation law for matrices state?
22. If matrices A and B are added and C is subtracted, which property ensures that \(A + (B - C) = (A + B) - C\)?
23. When can two matrices A and B be multiplied?
24. Which property of matrix multiplication states that \((AB)C = A(BC)\)?
25. Which property of matrix multiplication states that \(A(B + C) = AB + AC\)?
26. Which property of matrix multiplication states that \((A + B)C = AC + BC\)?
27. What does the Identity Law for matrices state?
28. If matrices A and B are such that the number of columns in A is equal to the number of rows in B, which operation is valid?
29. Which property of matrix multiplication is used to solve \((AB)C = A(BC)\)?
30. Which property of matrix multiplication allows us to write \(A(B + C) = AB + AC\)?
31. Which property of matrix multiplication allows us to write \((A + B)C = AC + BC\)?
32. If \(A\) is a 2x3 matrix and \(B\) is a 3x4 matrix, what is the dimension of the product \(AB\)?
33. What is the transpose of a matrix?
34. Which of the following represents the transpose of matrix A?
35. Which property of the transpose states that \((A')' = A\)?
36. Which property of the transpose states that \((kA)' = kA'\), where k is a scalar?
37. Which property of the transpose states that \((A + B)' = A' + B'\)?
38. Which property of the transpose states that \((AB)' = B'A'\)?
39. If matrix A is a 3x2 matrix, what will be the dimensions of \(A'\) (the transpose of A)?
40. Given two matrices A and B, which of the following is true regarding their transposes?
41. If \(A'\) is the transpose of matrix A, what is the result of transposing \(A'\) again?
42. What happens when the transpose of a matrix is multiplied by a scalar \(k\)?
43. What is the rank of a matrix?
44. The rank of a matrix A is denoted by which symbol?
45. What must be true about the minors of order r+1 for a matrix to have rank r?
46. For a matrix A to have a rank r, what condition must a minor of order r satisfy?
47. Which of the following statements is true regarding the rank of a matrix?
48. If every square sub-matrix of order r+1 is singular, what does this imply about the rank r of the matrix?
49. What does it mean if a matrix has a rank of zero?
50. For a matrix A with rank r, what can be said about its square sub-matrix of order r+1?
51. Which of the following is a correct method to determine the rank of a matrix?
52. Which of the following conditions does not directly relate to determining the rank of a matrix?