In algebra, the determinant is useful value that can be computer from the elements of a square matrix. The determinant is represented as det 'A' or `|A|` and its value can be evaluated by the expansion of the determinant as given below
(A) Expansion of two order determinant :
(B) Expansion of `3^(rd)` order determinant
(i) With respect to first fow :
`|A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=a_(1)|{:(b_(1),c_(2)),(b_(x3,c_(3)):}|+b_(1)|{:(a_(2),c_(2)),(a_(2),c_(2)):}|+c_(1)|{:(b_(x),c_(2)),(b_(2),c_(2)):}|`
`=a_(1)(b_(2)c_(3)-b_(3)c_(2))-b_(1)(a_(2)c_(3)-a_(3)c_(2))+c_(1)(a_(2)b_(3)-b_(2)a_(3))`
(ii) With respect to second column :
`|A|=|{:(a_(1),b_(1),c_(1)),(a_(2),b_(2),c_(2)),(a_(3),b_(3),c_(3)):}|=-b_(1)|{:(a_(2),c_(1)),(a_(3),c_(3)):}|+b_(2)|{:(a_(1),c_(1)),(a_(3),c_(3)):}|-b_(3)|{:(a_(1),c_(1)),(a_(2),c_(2)):}|`
Similarly a determinant can be expanded with respect to any row or column
The value of for which determinant `|{:(2,3,-1),(-1,-2,k),(1,-4,1):}|` vanishes, is

Options

A. `-3`
B. 7/11
C. `-2`
D. 2