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

Options

A. [z]
B. [y]
C. [x]
D. none of these

Answer

A

Explanation

We have, `[x] = -1, [y] = 0 and [z] =1`
`:. |([x] +1,[y],[z]),([x],[y] +1,[z]),([x],[y],[z] +1)| = |(0,0,1),(-1,1,1),(-1,0,2)| = 1 = [z]`