AERO GATE TOPPER
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Linear Algebra
AERO GATE TOPPER
1. If matrix A has a rank of 2, what is the rank of the matrix formed by multiplying A with a 2x2 invertible matrix B?
2. Given the matrix A
3. For a matrix A with eigenvalues 2, -3, and 5, what is the determinant of A?
4. If a matrix A satisfies A² - A = 0, where A is a 2x2 matrix, how many distinct eigenvalues does A have?
5. Which of the following statements is true for an invertible matrix A?
6. Let
7. What is the rank of the following matrix?
8. What is the characteristic polynomial of the matrix D =
9. Which of the following is true for any two orthogonal vectors
10. Which of the following is NOT a property of a linear transformation?
11. Which of the following statements about the null space of a matrix A is TRUE?
12. Which of the following matrices does NOT have an inverse?
13. Calculate the determinant of the matrix
14. What are the eigenvalues of the matrix G =
15. What is the purpose of the Gram-Schmidt process?
16. How do you calculate the characteristic polynomial of a matrix A?
17. What does the Cayley-Hamilton theorem state?
18. Find the number of non-zero singular values for the matrix
19. What is the Jordan normal form of a matrix used for?
20. What does RREF stand for in the context of linear systems?
21. Which of the following correctly defines a vector space?
22. What is the purpose of the Gram-Schmidt process?
23. What characterizes a nilpotent matrix?
24. Which property defines an orthogonal matrix?
25. What does the spectral theorem state for symmetric matrices?
26. What does the rank-nullity theorem state?
27. How is an eigenvalue defined for a matrix A?
28. When is a matrix considered diagonalizable?
29. Which of the following is a property of a linear transformation?
30. How is the characteristic polynomial of a matrix A defined?
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