InterviewSolution
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InterviewSolution
This section includes InterviewSolutions, each offering curated multiple-choice questions to sharpen your knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Let `Ma n dN`be two `3xx3`non singular skew-symmetric matrices such that `M N=N Mdot`If `P^T`denote the transpose of `P ,`then `M^2N^2(M^T N^(-1))^T`is equal to`M^2`b. `-N^2`c. `-M^2`d. `M N`A. `M^(2)`B. `-N^(2)`C. `-M^(2)`D. MN |
| Answer» Correct Answer - C | |
| 52. |
Let M be a 2 x 2 symmetric matrix with integer entries . Then , M is invertible , ifA. the first columb of M is the traspose of the second row of MB. the second row of M is the transpose of first column of MC. M is a diagonal matrix with nonzero entrires in the main diagonalD. the product of entries in the main diagonal of M is not the square of an integer |
| Answer» Correct Answer - C::D | |
| 53. |
Let m and N be two 3x3 matrices such that MN=NM. Further if `M!=N^2` and `M^2=N^4` then which of the following are correct.A. determinant of `(M^(2)+MN^(2))` is 0B. there is a `3xx3 ` non-zero matrix U such that `(M^(2)+MN^(2))` U is the zero matrixC. determinant of `(M^(2)+MN^(2))ge1`D. for a `3xx3` matrix U, if `(M^(2)+MN^(2))U` equals the zero matrix then U is the zero matrix |
| Answer» Correct Answer - A::B | |
| 54. |
Let a, b, c be suchthat `b(a""+""c)!=0`. If`|a a+1a-1-bb+1b-1cc-1c+1|+|a+1b+1c-1a-1b-1c+1(-1)^(n+2)a(-1)^(n+1)b(-1)^n c|=0`then the value of n is(1) zero (2) any even integer(3) any oddinteger (4) any integerA. zeroB. any even integerC. any odd integerD. any integer |
| Answer» Correct Answer - C | |
| 55. |
If the adjoint of a `3 xx 3` matrix P is `[{:(,1,4,4),(,2,1,7),(,1,1,3):}]`, then the possible value(s) of the determinant of P is (are)A. `-2`B. `-1`C. 1D. 2 |
| Answer» Correct Answer - A::D | |
| 56. |
Let `A=((1,0,0),(2,1,0),(3,2,1))`. If `u_(1)` and `u_(2)` are column matrices such that `Au_(1)=((1),(0),(0))` and `Au_(2)=((0),(1),(0))`, then `u_(1)+u_(2)` is equal to :A. `({:(,-1),(,1),(,0)):}`B. `({:(,-1),(,1),(,-1)):}`C. `({:(,-1),(,-1),(,0)):}`D. `({:(,1),(,-1),(,-1)):}` |
| Answer» Correct Answer - D | |