If [`` ] denotes the greatest integer less than or equal to the real number under consideration, and `-1lt=x<0,0ley<1,1lt=z<2,` then find the value of the following determinant: `|[[x]+1,[y],[z]],[[x],[y]+1,[z]],[[x],[y],[z]+1]|` (A) 0 (B) 1 (C) 2 (D) 3

Explanation

Given:`-1lt=x<0`

`implies [x]=-1`

`0ley<1`

`implies [y]=0`

`1lt=z<2`

`implies [z]=1`

Then the value of

`|[[x]+1,[y],[z]],[[x],[y]+1,[z]],[[x],[y],[z]+1]|`is

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