InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Consider a matrix `A=[a_("ij")]` of order `3xx3` such that `a_("ij")=(k)^(i+j)` where `k in I`. Match List I with List II and select the correct answer using the codes given below the lists. A. `{:(a,b,c,d),(r,p,s,q):}`B. `{:(a,b,c,d),(s,p,q,r):}`C. `{:(a,b,c,d),(r,p,q,s):}`D. `{:(a,b,c,d),(q,p,r,s):}` |
|
Answer» Correct Answer - C Let `A=[A_("ij")]_(3xx3)`, where `a_("ij")=(k)^(i+j)` So, `A=[(k^(2),k^(3),k^(4)),(k^(3),k^(4),k^(5)),(k^(4),k^(5),k^(6))]` a. If A is singular, then `|A|=0` `implies k^(2).k^(3).k^(4) |(1,1,1),(k,k,k),(k^(2),k^(2),k^(2))|=0`, `implies k in I` b. If A is null matrix, then `k in {0}` c. There is no value of `k` for `A` to be skew-symmetric matrix which is not null-matrix. `:. k in phi` d. If `A^(2)=3A`, then `[(k^(2),k^(3),k^(4)),(k^(3),k^(4),k^(5)),(k^(4),k^(5),k^(6))][(k^(2),k^(3),k^(4)),(k^(3),k^(4),k^(5)),(k^(4),k^(5),k^(6))]=[(3k^(2),3k^(3),3k^(4)),(3k^(3),3k^(4),3k^(5)),(3k^(4),3k^(5),3k^(6))]` `implies [(k^(4)+k^(6)+k^(8),k^(5)+k^(7)+k^(9),k^(6)+k^(8)+k^(10)),(k^(5)+k^(7)+k^(9),k^(6)+k^(8)+k^(10),k^(7)+k^(9)+k^(11)),(k^(6)+k^(8)+k^(10),k^(7)+k^(9)+k^(11),k^(8)+k^(10)+k^(12))]` `=[(3k^(2),3k^(3),3k^(4)),(3k^(3),3k^(4),3k^(5)),(3k^(4),3k^(5),3k^(6))]` `implies k in {-1, 0, 1}` |
|