16. Let the eigen values of a 2 x 2 matrix A be 1, -2 with eigen vectors x_{1} and x_{2} respectively. Then the eigen values and eigen vectors of the matrix A^{2} – 3A + 4I would, respectively, be

- 2, 14; x
_{1}, x_{2} - 2, 14; x
_{1}+ x_{2}, x_{1}– x_{2} - 2, 0; x
_{1}, x_{2} - 2, 0; x
_{1}+ x_{2}, x_{1}– x_{2}

17. Two eigen values of a 3 x 3 real matrix P are and 3. The determinant of P is

- 5
- 10
- 15
- 20

18. Consider a 2 x 2 square matrix

where x is unknown. If the eigen values of the matrix A are (σ + jω) and (σ – jω), then x is equal to

- + jω
- – jω
- + ω
- – ω

19. The condition for which the eigen values of the matrix are positive, is

- k > 1/2
- k > -2
- k > 0
- k < -1/2

20. Consider a 3 x 3 matrix with every element being equal to 1. Its only non-zero eigen value is

- 1
- 2
- 4
- 3

21. If the entries in each column of a square matrix M add up to 1, then an eigen value of M is

- 4
- 3
- 2
- 1

22. Consider the following 2 x 2 matrix A where two elements are unknown and are marked by a and b. The eigen values of this matrix are -1 and 7. What are the values of a and b?

- a = 6, b = 4
- a = 4, b = 6
- a = 3, b = 5
- a = 5, b = 3

23. The value of x for which all the eigen-values of the matrix given below are real is

- 5 + j
- 5 – j
- 1 – 5j
- 1 + 5j

24. At least one eigen value of a singular matrix is

- positive
- zero
- negative
- imaginary

25. The two eigen values of the matrix have a ratio of 3 : 1 for p = 2. What is another value of p for which the eigen values have the same ratio of 3 : 1?

- -2
- 1
- 7/3
- 14/3

26. The larger of the two eigen values of the matrix is

- 4
- 6
- 1
- 2

27. The value of p such that the vector is an eigen vector of the matrix is

- 17
- 16
- 15
- 14

28. The lowest eigen value of the 2 x 2 matrix is

- 5
- 2
- 3
- 4

29. The smallest and largest eigen values of the following matrix are

- 1.5 and 2.5
- 0.5 and 2.5
- 1 and 3
- 1 and 2

30. In the given matrix , one of the eigen values is 1. The eigen vectors corresponding to the eigen value 1 are

- {α(4,2,1) | α ≠ 0, α ∈ R}
- {α(-4,2,1) | α ≠ 0, α ∈ R}
- {α(,0,1) | α ≠ 0, α ∈ R}
- {α(,0,1) | α ≠ 0, α ∈ R}