Eigenvalues MCQ’s

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This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Eigenvalues”.

1. Find the Eigen values of matrix A = \begin{bmatrix} 2 & 1 & 0\\ 1 & 2 & 1\\ 0 & 1 & 2\\ \end{bmatrix}.

a) 2 + \sqrt{2}, 2-\sqrt{2}, 2
b) 2, 1, 2
c) 2, 2, 0
d) 2, 2, 2

2. Find the product of Eigen values of a matrix A = \begin{bmatrix} 1 & 2 & 4\\ 0 & 6 & 0\\ 3 & 1 & 2\\ \end{bmatrix}.

a) 60
b) 45
c) -60
d) 40

3.Let us consider a square matrix A of order n with Eigen values of a, b, c then the Eigen values of the matrix AT could be.
a) a, b, c
b) -a, -b, -c
c) a-b, b-a, c-a
d) a-1, b-1, c-1

4. Let the matrix A be the idempotent matrix then the Eigen values of the idempotent matrix are ________
a) 0, 1
b) 0
c) 1
d) -1

5. Find the sum of the Eigen values of the matrix A = \begin{bmatrix} 3 & 6 & 7\\ 5 & 4 & 2\\ 7 & 9 & 1\\ \end{bmatrix}.

a) 7
b) 8
c) 9
d) 10

6. The Eigen values of a 3×3 matrix are λ1, λ2, λ3 then the Eigen values of a matrix A3 are __________
a) λ1, λ2, λ3
b) \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}
c) λ_1^3, λ_2^3, λ_3^3
d) 1, 1, 1

7. What is Eigen value?
a) A vector obtained from the coordinates
b) A matrix determined from the algebraic equations
c) A scalar associated with a given linear transformation
d) It is the inverse of the transform

8. Let us consider a 3×3 matrix A with Eigen values of λ1, λ2, λ3 and the Eigen values of A-1 are?
a) λ1, λ2, λ3
b) \frac{1}{λ_1}, \frac{1}{λ_2}, \frac{1}{λ_3}
c) -λ1, -λ2, -λ3
d) λ1, 0, 0

9. Find the Eigen values of matrix A=\begin{bmatrix} 4 & 1 \\ 1 & 4 \\ \end{bmatrix} .

a) 3, -3
b) -3, -5
c) 3, 5
d) 5, 0

10. Where do we use Eigen values?
a) Fashion or cosmetics
b) Communication systems
c) Operations
d) Natural herbals

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