If s=(a+b+c),then value of `|{:(s+c,a,b),(c,s+a,b),(c,a,s+b):}|`is

Options

A. `2s^(2)`
B. `2s^(3)`
C. `s^(3)`
D. `3s^(3)`

Answer

B

Explanation

We have,
`Delta = |(s +c,a,b),(c,s +a,b),(c,a,s +b)|`
`rArr Delta = |(s +a + b + c,a,b),(s +a + b + c,s +a,b),(s +a + b +c,a,s +b)| " " [("Applying " C_(1) rarr C_(1)),(" " + C_(2) + C_(3))]`
`rArr Delta = (s +a + b +c) |(1,a,b),(1,s +a,b),(1,a,s +b)|`
`rArr Delta = 2s|(1,a,b),(0,s,0),(0,0,s)| " " [("Applying" R_(2) rarr R_(2) - R_(1)),(" "R_(3) rarr R_(3) - R_(1))]`
`rArr Delta = 2s^(3)`