1. What is the determinant of 1.9 2.11 3.17 4.19

2. What is the determinant of 1.0 2.28 3.44 4.-28

3. Which matrix represents the following system of equations? x = 4 y = 7 1. 2. 3.

4. What is the solution to the following system of equations? x 1 + x 2 = 3 2x 1 - 6x 2 = -10 1.x 1 =-9/8 and x 2 =-30/8 2.x 1 =4 and x 2 =5 3.x 1 =1 and x 2 =2 4.x 1 =1 and x 2 =½ 5.There are an infinite number of solutions 6.There are no solutions

5. What is the solution to the following system of equations? 6x 1 + 9x 2 = 3 2x 1 + 3x 2 = 5 1.x 1 =2 and x 2 =0 2.x 1 =0 and x 2 =1/3 3.x 1 =1 and x 2 =-1/3 4.x 1 =-5/2 and x 2 =2 5.There are an infinite number of solutions 6.There are no solutions

6. Which of the following statements are true? ( A) sum of eigenvalues = sum diagonal elements (trace) (B) product of eigenvalues = determinant of square matrix A (C) distinct eigenvalues = linearly dependent eigenvectors 1.Only (A) 2.Only (B) 3.Only (C) 4.Both (A) and (B) 5.Both (A) and (C) 6.Both (B) and (C) 7.(A), (B) and (C)

7. Which of the following statements is true? 1. 2. 3. 4.

8. Dominant eigenvalue = eigenvalue with largest magnitude 1.True 2.False 3.Don’t Know

9. What is the characteristic equation of the following matrix? 1.λ² - 7λ + 6 = 0 2.λ² - 7λ + 14 = 0 3.λ² - 7λ - 2 = 0 4.None of the above

10. What are the eigenvalues of 1.2 and 4 2.0 and 4 3.0 and 2 4.6 and 8

11. What are the eigenvalues of the following matrix? 1.λ = 2, 4 2.λ = 2, 6 3.λ = 2, 8 4.λ = 4, 8

12. What are the eigenvalues for the following matrix? 1.λ = -5, 0, 5 2.λ = -5, 5, 10 3.λ = 0, 5, 5 4.λ = 5, 5, 10

13. What are the eigenvalues for the following matrix? 1. λ = -2, 3, 4 2.λ = -6, -2, 3 3.λ = -2, 3, 6 4.λ = -6, -3, 2

14. Matrix A given below has eigenvalues λ = 2, 4, 6. Without further calculation write down the eigenvalues for. 1. 2. 3. 4.

15. Which of the vectors below is an eigenvector, corresponding to the eigenvalue λ= 7 of the matrix 1. 2. 3. 4.

16. Which of the vectors below is an eigenvector, corresponding to the eigenvalue λ= 3 of the matrix 1. 2. 3. 4.

17. What are the eigenvectors of the following matrix? 1. 2. 3. 4.

18. Which of the following shows the eigenvectors for matrix A? 1. 2. 3. 4.

19. Which set of vectors is linearly independent? 1.(1,6), (3,18) 2.(1,2), (3,4) 3.None of the above 4.Both of the sets

20. Normalise the eigenvector X. 1. 2. 3. 4.

21. Diagonalization means which of the following? 1.Adding the diagonal elements of a matrix. 2.Multiplying the diagonal elements of a matrix. 3.Transforming a non-diagonal matrix. 4.None of the above.

22. Why might we want to diagonalize a matrix? 1.Computing powers of the matrix becomes easy. 2.Easy to find eigenvalues of a diagonal matrix. 3.Both of these reasons. 4.None of these reasons

23. You can always diagonalize an n x n matrix with n distinct eigenvalues. 1.True 2.False 3.Don’t Know

24. Below are eigenvectors of four 2x2 matrices. Which matrix is definitely diagonalizable? 1. 2. 3. 4.

25. Obtain the modal matrix P. 1. 2. 3. 4.

26. The matrix A= has eigenvalues - 1 and 2 with respective eigenvectors If calculate. 1.2. 3. 4.

27. What is A² ? 1. 2. 3. 4.

28. What is ? 1. 2. 3. 4.

29. The eigenvalues of a symmetric matrix with real elements are... 1.Always complex 2.Always real 3.Either complex or real

30. Which of the following is a symmetric matrix? 1. 2. 3. 4.

31. A square matrix A is said to be orthogonal if 1.True 2.False 3.Don’t Know

32. Two n x 1 column vectors X and Y are orthogonal if XY=0 1.True 2.False 3.Don’t Know

33. The eigenvalues of a symmetric matrix A are λ =0 and λ =10 X and Y are the eigenvectors for λ =0 and λ =10 respectively. Are X and Y orthogonal? 1.Yes 2.No 3.Don’t Know

34. An Hermitian matrix is one satisfying 1.True 2.False 3.Don’t Know

35. Is the following matrix Hermitian? 1.Yes 2.No 3.Don’t Know

36. Separating the variables in gives 1. 2. 3. 4.

37. Write in matrix form the pair of coupled differential equations 1. 2. 3. 4.

38. Find the solution of the coupled differential equations with initial conditions x(0)=1 and y(0)=3 1. 2. 3. 4.

39. Given. What is the general solution to a system of 2 nd order differential equations for the negative eigenvalues ? 1. 2. 3. 4.

40. An elastic membrane in the plane with boundary circle is shown below. principle direction

41. The membrane is stretched so the point P:( ) goes over the point Q:( ) where Find the amount that the principle directions are stretched by 1.By factors 3 and 11. 2.By factors 7 and 4. 3.By factors 4 and 4. 4.By factors 7 and 7. 5.Don’t Know