MCQOPTIONS
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MCQOPTIONS
This section includes 10 Mcqs, each offering curated multiple-choice questions to sharpen your Eigen Values and Eigen Vectors knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
Which among the following is not a type of quadratic form? |
| A. | Positive Semi-definite |
| B. | Negative definite |
| C. | Partial definite |
| D. | Indefinite |
| Answer» D. Indefinite | |
| 2. |
The Canonical form is also known as sum of squares form. |
| A. | False |
| B. | True |
| Answer» C. | |
| 3. |
Write the expression for spur of a matrix for a 3 3 matrix whose entries are in the form of aij. |
| A. | a<sub>11</sub>+ a<sub>12</sub>+a<sub>13</sub> |
| B. | a<sub>11</sub>+ a<sub>21</sub>+a<sub>31</sub> |
| C. | a<sub>12</sub>+ a<sub>22</sub>+a<sub>32</sub> |
| D. | a<sub>11</sub>+ a<sub>22</sub>+a<sub>33</sub> |
| Answer» E. | |
| 4. |
Reduce the quadratic form to canonical form, (3x_1^2+ 2x_2^2+8x_{12}+8x_{23}+8x_{31}=0 ). |
| A. | ( begin{bmatrix}3 & 4 & 4 4 & 0 & 4 4 & 4 & 2 end{bmatrix} ) |
| B. | ( begin{bmatrix}3 & 4 & 4 4 & 2 & 0 4 & 4 & 0 end{bmatrix} ) |
| C. | ( begin{bmatrix}3 & 4 & 4 4 & 2 & 4 4 & 4 & 0 end{bmatrix} ) |
| D. | ( begin{bmatrix}3 & 4 & 0 4 & 2 & 4 4 & 4 & 0 end{bmatrix} ) |
| Answer» D. ( begin{bmatrix}3 & 4 & 0 4 & 2 & 4 4 & 4 & 0 end{bmatrix} ) | |
| 5. |
If A is a matrix, such that, Ak = 0, for positive integer k, then, A is known as Nilpotent matrix. |
| A. | True |
| B. | False |
| Answer» B. False | |
| 6. |
What is the index of the quadratic form, (3x_1^2+ x_3^2+8x_{13}+ 9x_{21}+ 2x_{23}=0 )? |
| A. | 2 |
| B. | 4 |
| C. | 3 |
| D. | 1 |
| Answer» B. 4 | |
| 7. |
What is the signature of the quadratic form, (Q = 7x_1^2+ 2x_2^2- 3x_3^2+x_{31}+ x_{23}=0 )? |
| A. | 2 |
| B. | -2 |
| C. | 1 |
| D. | -1 |
| Answer» D. -1 | |
| 8. |
Determine the nature of the given matrix. ( begin{bmatrix}2 & 0 & 0 1 & 2 & 1 0 & 0 & 1 end{bmatrix} ) |
| A. | |
| B. | Indefinite |
| C. | Positive definite |
| D. | Negative definite |
| E. | Positive semi-definite |
| Answer» C. Positive definite | |
| 9. |
Signature of a quadratic form is the difference between the positive and negative terms in the canonical form. |
| A. | True |
| B. | False |
| Answer» C. | |
| 10. |
Which of the following is not a condition for a given real nonsingular quadratic form, Q = XTAX, to be a negative definite quadratic form? |
| A. | The number of positive square terms in the quadratic form is equal to zero |
| B. | The rank of the matrix A is equal to the number of variables in the quadratic form (index) |
| C. | All the eigen values of A are negative |
| D. | The rank and index are equal |
| Answer» E. | |