MCQOPTIONS
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MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Signals Systems knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
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 |
| Answer» D. 5, 0 | |
| 2. |
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 |
| Answer» D. 1, 1, 1 | |
| 3. |
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 |
| Answer» C. -λ1, -λ2, -λ3 | |
| 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 |
| Answer» B. 0 | |
| 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 |
| Answer» C. 9 | |
| 6. |
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 |
| Answer» B. -a, -b, -c | |
| 7. |
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 |
| Answer» D. 40 | |
| 8. |
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 |
| Answer» B. 2, 1, 2 | |