1. Tardigrade
  2. Question
  3. Mathematics
  4. If [ ] denotes the greatest integer less than or equal to the real number under consideration and -1 le x < 0; 0 le y < 1; 1 le z < 2 , then the value of the determinant |[x]+1&[y]&[z] [x]&[y]+1&[z] [x]&[y]&[z]+1| is

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Q. If [ ] denotes the greatest integer less than or equal to the real number under consideration and $-1 \le x < 0; 0 \le y < 1; 1 \le z < 2 $ , then the value of the determinant
$\begin{vmatrix}\left[x\right]+1&\left[y\right]&\left[z\right]\\ \left[x\right]&\left[y\right]+1&\left[z\right]\\ \left[x\right]&\left[y\right]&\left[z\right]+1\end{vmatrix}$ is

BITSATBITSAT 2016

Solution:

Since, $-1 \leq x<0$
$\therefore [x]=-1$
$0 \leq y<1 \therefore [y]=0$
$1 \leq z<2 \therefore [z]=1$
$\therefore $ Given determinant = $\begin{vmatrix}0&0&1\\ -1&1&1\\ -1&0&2\end{vmatrix}$
$ = 1 = [z] $