If [] denotes the greatest integer less than or equal to the real number under consideration and `-1lt=xlt0,0lt=ylt1,1lt=zlt2,` the value of the determinant `|{:([x]+1,[y],[z]),([x],[y]+1,[z]),([x],[y],[z]+1):}|` is

Explanation

As, `-1 le x lt 0 => [x] = -1`

As, `0 le y lt 1 => [y] = 0`

As, `1 le z lt 2 => [z] = 1`

So, the given determinant becomes,

`|[-1+1,0,1],[-1,0+1,1],[-1,0,1+1]|`

`=|[0,0,1],[-1,1,1],[-1,0,2]|`

`=[0-0+1(0+1)] = 1`

So, value of the given determinant is `1`.