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Let a,b,c be such that b(a+c)ne 0. If |{...

Let a,b,c be such that b(a+c)`ne 0`. If `|{:(,a,a+1,a-1),(,-b,b+1,b-1),(,c,c-1,c+1):}|+|{:(,a+1,b+1,c-1),(,a-1,b-1,c+1),(,(-1)^(n+2)a,(-1)^(n+1)b,(-1)^(n)c):}|=0`, Then the value of 'n' is:

A

zero

B

any even integer

C

any odd integer

D

any integer

Text Solution

Verified by Experts

The correct Answer is:
3
`|{:(a,,a+1,,a-1),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n) |{:(a+1,,b+1,,c-1),(a-1,,b-1,,c+1),(a,,-b,,c):}|`
`= |{:(a,,a+1,,a-1),(-b,,b +1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n) |{:(a+1,,a-1,,a),(b+1,,b-1,,c+1),(c-1,,c+1,,c):}|`
`= |{:(a,,a+1,,a-10),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|+(-1)^(n+2) |{:(a,,a+1,,a-1),(-b,,b+1,,b-1),(c,,c-1,,c+1):}|`
this is eqaul to zero only in n+2 i sodd i.e., n is an odd integer
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