If `a-2b+c=1`, then the value of `|{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}|` is

Options

A. `x`
B. `-x`
C. `-1`
D. `1`

Answer

C

Explanation

`(c )` `|{:(x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x+c):}|`
Applying `R_(1)toR_(1)-2R_(2)+R_(3)`
`|{:(0,0,1),(x+2,x+3,x+b),(x+3,x+4,x+c):}| ( :' a-2b+c=1)`
Applying `R_(3)toR_(3)-R_(2)`,
the determinant reduces to
`|{:(0,0,1),(x+2,x+3,x+b),(1,1,c-b):}|=-1`