InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Let M be a `2xx2` symmetric matrix with integer entries. Then , M is invertible, ifA. the first column of M is the transpose of the second row of MB. The second row of M is the transpose of the first column of MC. m is a diagonal matrix with non- zero entries 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 Let `M= [[a,b],[c,d]]`, where `a, b, c, in I` M is invertible if `abs((a,b),(b,c)) ne 0 rArr ac- b^(2) ne 0 ` (a) `[[a],[b]]=[[b],[c]]rArr a = b =c rArr ac-b^(2)=0` `therefore` Option (a) is incorrect (b) `[(b,c)]= [(a,b)] rArr a = b = c rArr ac - b^(2) = 0` `therefore` Option (b) is incorrect (c) `M= [[a,0],[0,c]], ` then` abs(M) = ac ne 0` `therefore` M is invertible `therefore` Potion ( c) is correct. (d) As `acne"Integre """^(2)rArrac ne b^(2)` `therefore ` Option (d)is correct. |
|