if y= sin mx, them the value of the determinant
`|{:(y,,y_(1),,y_(2)),(y_(3),,y_(4),,y_(5)),(y_(6),,y_(7),,y_(8)):}|" Where " y_(n)=(d^(n)y)/(dx^(n)) " is "`

Options

A. `m^(9)`
B. `m^(2)`
C. `m^(3)`
D. 0

Answer

D

Explanation

We have y= sin mx , therefore `y_(1) =m cos mx y_(2) =m^(2)` sin mx etc.
`Delta = |{:(y,,y_(1),,y_(2)),(y_(3),,y_(4),,y_(5)),(y_(6),,y_(7),,y_(8)):}|`
`=|{:(sin mx ,,m cos mx,,-m^(2) sin mx),(-m^(2) cos mx,,m^(4) sin mx,,m^(5) cos mx),(-m^(6) sin mx,,-m^(7) cos mx,,m^(8) sin ms):}|`
`=m^(12) |{:(sin mx ,,cos mx,,-sin mx),(-cos mx,,sin mx,,cos mx),(-sin mx,,-cos m,,sin mx):}|=0`