MCQOPTIONS
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MCQOPTIONS
This section includes 9 Mcqs, each offering curated multiple-choice questions to sharpen your Simultaneous Algebraic Equations knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
For a matrix A having |A| = 0, which of the following are true? |
| A. | A<sup>-1</sup> exists |
| B. | A<sup>-1</sup> does not exists |
| C. | A is non-singular |
| D. | A<sup>-1</sup> exists with |A<sup>-1</sup>|= 0 |
| Answer» C. A is non-singular | |
| 2. |
If A and B are two square matrices, then |A.B| is same as which of the following? |
| A. | |A|.|B| |
| B. | |B|.|A| |
| C. | |B-A| |
| D. | |A-B| |
| Answer» B. |B|.|A| | |
| 3. |
A matrix B and _____ will have the same determinant. |
| A. | Its transpose |
| B. | Its inverse |
| C. | Its echelon matrix |
| D. | Its adjoint |
| Answer» B. Its inverse | |
| 4. |
Consider the set P of all determinants of order 3 with entries 0 or 1 only. Let Q the subset of P consisting of all determinants with value 1.Let R be the subset of P consisting of all determinants with value 1. Then, which of the following is true? |
| A. | R is empty |
| B. | Q has as many elements as R |
| C. | P = Q R |
| D. | Q has twice as many elements as R |
| Answer» C. P = Q R | |
| 5. |
If each element of a line consists of m terms, the determinant can be expressed as the sum of ______ determinants. |
| A. | m-1 |
| B. | m |
| C. | m+1 |
| D. | m<sup>2</sup> |
| Answer» C. m+1 | |
| 6. |
A determinant vanishes if one of the entire row or column consists of all zero elements? |
| A. | True |
| B. | False |
| Answer» C. | |
| 7. |
What is the value of the determinant ( begin{pmatrix}2&5&1 7&4&5 1&2&3 end{pmatrix} )? |
| A. | -56 |
| B. | -96 |
| C. | -66 |
| D. | -85 |
| Answer» D. -85 | |
| 8. |
For a determinant ( begin{vmatrix}a&b&c d&e&f g&h&i end{vmatrix} ), the cofactor of h will be equal to which of the following? |
| A. | (-1)<sup>3+2</sup> ( begin{vmatrix}a&c d&f end{vmatrix} ) |
| B. | (-1)<sup>3+2</sup> ( begin{vmatrix}d&f g&i end{vmatrix} ) |
| C. | (-1)<sup>3+2</sup> ( begin{vmatrix}a&c g&i end{vmatrix} ) |
| D. | (-1)<sup>3+2</sup> ( begin{vmatrix}b&c e&f end{vmatrix} ) |
| Answer» B. (-1)<sup>3+2</sup> ( begin{vmatrix}d&f g&i end{vmatrix} ) | |
| 9. |
For a determinant containing 4 elements a1 b1 a2 b2, what will the elements of the leading diagonal? |
| A. | a<sub>1</sub> b<sub>1</sub> |
| B. | a<sub>1</sub> b<sub>2</sub> |
| C. | a<sub>2</sub> b<sub>1</sub> |
| D. | a<sub>2</sub> b<sub>2</sub> |
| Answer» C. a<sub>2</sub> b<sub>1</sub> | |