InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
If `A = [[0, 1],[3,0]]and (A^(8) + A^(6) + A^(4) + A^(2) + I) V= [[0],[11]],` where `V` is a vertical vector and `I` is the `2xx2` identity matrix and if `lambda` is sum of all elements of vertical vector `V`, the value of `11 lambda` is |
|
Answer» Correct Answer - 1 `because A =[[0,1],[3,0]]` `therefore A^(2) = A cdot A = [[0,1],[3,0]] [[0,1],[3,0]]= [[3,0],[0,3]]= 3I` `rArr A^(4) = (A^(2))^(2) = 9 I , A^(6) = 27I, A^(8) = 81 I` Now, `(A^(8) + A^(6) + A^(4)+ A^(2) + I) V = (121) IV = (121) V" "...(i)` `(A^(8) + A^(6) + A^(4)+ A^(2) + I) V = [[0],[11]]" " (ii) ` From Eqs. (i) and (ii), `(121) V = [[0],[11]]rArr V = [[0],[1/11]]` `therefore` Sun of elements of `V= 0 + 1/11 = 1/11 = lambda` [given] `therefore 11 lambda = 1` |
|