Let `|(a,l,m),(l,b,n),(m,n,c)||(bc-n^2,mn-lc,ln-bm),(mn-lc,ac-m^2,ml-an),(ln-bm,lm-an,ab-l^2)|=64.` If the value of `|(2a+3l,3l+5m,5m+4a),(2l+3b,3b+5n,5n+4l),(2m+3n,3n+5c,5c+4m)|=lambda` then `[lambda/2]` equals

Options

A. `120`
B. `240`
C. `360`
D. `480`

Answer

C

Explanation

`(c )` `DeltaDelta^(2)=64`
`impliesDelta^(3)=64impliesDelta=4`
`|{:(2a+3l,3l+5m,5m+4a),(2l+3b,3b+5n,5n+4l),(2m+3n,3n+5c,5c+4m):}|`
`=[(2xx3xx5)+(3xx5xx4)]Delta`
`=(30+60)Delta`
`=90(4)`
`=360`