MCQOPTIONS
Saved Bookmarks
MCQOPTIONS
This section includes 8 Mcqs, each offering curated multiple-choice questions to sharpen your Linear Algebra knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
The sum of two skew-symmetric matrices is also a skew-symmetric matrix. |
| A. | False |
| B. | True |
| Answer» C. | |
| 2. |
Find the symmetric matrix for the given quadratic form, \(Q = 2x_1^2 + 2x_2^2 + 5x_3^2 – 3x_1 x_2+7x_3 x_1.\) |
| A. | \(\begin{bmatrix} 1 & \frac{-7}{2} & \frac{3}{2} \\ \frac{-7}{2} & 2 & 0 \\ \frac{3}{2} & 0 & \frac{5}{2}\end{bmatrix} \) |
| B. | \(\begin{bmatrix} 1 & \frac{-3}{2} & \frac{7}{2} \\ \frac{-3}{2} & 2 & 0 \\ \frac{7}{2} & 0 & \frac{5}{2}\end{bmatrix} \) |
| C. | \(\begin{bmatrix} 1 & \frac{3}{2} & \frac{-7}{2}\\ \frac{3}{2} & 2 & 0 \\ -\frac{7}{2} & 0 & \frac{5}{2}\end{bmatrix} \) |
| D. | \(\begin{bmatrix} 1 & \frac{-3}{2} & \frac{7}{2} \\ \frac{-3}{2} & 2 & 0 \\ \frac{7}{2} & 0 & 5\end{bmatrix} \) |
| Answer» C. \(\begin{bmatrix} 1 & \frac{3}{2} & \frac{-7}{2}\\ \frac{3}{2} & 2 & 0 \\ -\frac{7}{2} & 0 & \frac{5}{2}\end{bmatrix} \) | |
| 3. |
Which of the following matrix is 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. | \(\begin{bmatrix}0.33 & 0.67 & -0.67\\-0.67 & 0.67 & 0.33 \\0.67 & 0.33 & 0.67\end{bmatrix} \) |
| C. | \(\begin{bmatrix}0.33 & 0.67 & -0.67\\-0.67 & 0.67 & 0.33 \\ 0.67 & 0.33 & 0.67\end{bmatrix} \) |
| D. | \(\begin{bmatrix}0.33 & 0.67 & -0.67\\-0.67 & 0.67 & 0.33 \\0.67 & 0.33 & 0.67\end{bmatrix} \) |
| Answer» C. \(\begin{bmatrix}0.33 & 0.67 & -0.67\\-0.67 & 0.67 & 0.33 \\ 0.67 & 0.33 & 0.67\end{bmatrix} \) | |
| 4. |
Every Identity matrix is an orthogonal matrix. |
| A. | True |
| B. | False |
| Answer» C. | |
| 5. |
Find the values of x and y in the matrix below if the matrix is a skew symmetric matrix.P = \(\begin{bmatrix}0 & y & -4\\-5 & 0 & 8 \\ x+y&-8 & 0 \end{bmatrix} \) |
| A. | x = -1, y = 5 |
| B. | x = -9, y = -5 |
| C. | x = 9, y = 5 |
| D. | x = 1, y = -5 |
| Answer» B. x = -9, y = -5 | |
| 6. |
The matrix which remains unchanged under transposition is known as skew symmetric matrix. |
| A. | False |
| B. | True |
| Answer» B. True | |
| 7. |
Which among the following is listed under the law of transposes?a) (AT)T = AIb) (A*)* = A*c) (c |
| A. | (AT)T = AI |
| B. | (A*)* = A* |
| C. | (cA)T = cAT |
| D. | (AB)T = ATBT |
| Answer» D. (AB)T = ATBT | |
| 8. |
Who introduced the term matrix? |
| A. | James Sylvester |
| B. | Arthur Cayley |
| C. | Girolamo Cardano |
| D. | Paul Erdos |
| Answer» B. Arthur Cayley | |