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. |
The sum of two symmetric matrices is also a symmetric matrix. |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
Find the values of x and y in the matrix below if the matrix is a skew symmetric matrix.P = ( begin{bmatrix}0 & x+y & 6 3 & 0 & 9 x & 9 & 0 end{bmatrix} ) |
| A. | x = -6, y = 3 |
| B. | x = 3, y = 3 |
| C. | x = 6, y = -3 |
| D. | x = 0, y = 3 |
| Answer» D. x = 0, y = 3 | |
| 3. |
The determinant of the matrix whose eigen values are 7, 1, 9 is given by ________ |
| A. | 7 |
| B. | 63 |
| C. | 9 |
| D. | 17 |
| Answer» C. 9 | |
| 4. |
Which of the following matrix is not orthogonal? |
| A. | ( begin{bmatrix}0.33 & 0.67 & -0.67 -0.67 & 0.67 & 0.33 0.67 & 0.33 & 0.67 end{bmatrix} ) |
| B. | ( begin{bmatrix}cosx &sinx -sinx & cosx end{bmatrix} ) |
| C. | ( begin{bmatrix}0.33 & -0.67 & 0.67 0.67 & 0.67 & 0.33 -0.67 & 0.33 & 0.67 end{bmatrix} ) |
| D. | ( begin{bmatrix}cosx & sinx -sinx & -cosx end{bmatrix} ) |
| Answer» B. ( begin{bmatrix}cosx &sinx -sinx & cosx end{bmatrix} ) | |
| 5. |
Euler s integral of the first kind, which is a proper integral, is used to define the gamma function. |
| A. | True |
| B. | False |
| Answer» C. | |
| 6. |
Which of the following is true for matrices? |
| A. | (AB)<sup>-1</sup> = B<sup>-1</sup>A<sup>-1</sup> |
| B. | (A<sup>T</sup>) = A |
| C. | AB = BA |
| D. | A*I = I |
| Answer» B. (A<sup>T</sup>) = A | |
| 7. |
Which among the following does not belong to main types of integrals? |
| A. | Indefinite Integral |
| B. | Proper Definite Integral |
| C. | Improper Definite Integral |
| D. | Real Integral |
| Answer» E. | |
| 8. |
Which one of the following is not a criterion for linearity of an equation? |
| A. | The dependent variable y should be of second order |
| B. | The derivatives of the dependent variable should be of second order |
| C. | Each coefficient does not depend on the independent variable |
| D. | Each coefficient depends only on the independent variable |
| Answer» D. Each coefficient depends only on the independent variable | |
| 9. |
The solution of the given matrix equation is _____ ( begin{bmatrix}3 & 0 & 2 6 & 1 & 1 2 & 8 & 91 end{bmatrix} begin{bmatrix}x_1 x_2 x_3 end{bmatrix} begin{bmatrix}0 0 0 end{bmatrix} ) |
| A. | x<sub>1</sub> = 1, x<sub>2</sub> = 1, x<sub>3</sub> = 2 |
| B. | x<sub>1</sub> = 0, x<sub>2</sub> = 0, x<sub>3</sub> = 0 |
| C. | x<sub>1</sub> = 3, x<sub>2</sub> = -1, x<sub>3</sub> = -1 |
| D. | x<sub>1</sub> = 0, x<sub>2</sub> = -2, x<sub>3</sub> = 4 |
| Answer» C. x<sub>1</sub> = 3, x<sub>2</sub> = -1, x<sub>3</sub> = -1 | |
| 10. |
What is the canonical form of the matrix A = ( begin{bmatrix}1 & 0 1 & 1 end{bmatrix} )? |
| A. | x+xy+y<sup>2</sup> |
| B. | x<sup>2</sup>+xy |
| C. | x<sup>2</sup>+y<sup>2</sup> |
| D. | x<sup>2</sup>+xy+y<sup>2</sup> |
| Answer» E. | |