Determinants Matrices Question 18
Question: 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} [x]+1 & [y] & [z] \\ [x] & [y]+1 & [z] \\ [x] & [y] & [z]+1 \\ \end{vmatrix} $ is
Options:
A) $ [z] $
B) $ [y] $
C) [x]
D) None of these
Show Answer
Answer:
Correct Answer: A
Solution:
- [a] Since, $ -1<x<0 $
$ \therefore [x]=-1 $
$ 0<y<1\therefore [y]=0, $
$ 1<z<2\therefore [z]=1 $
$ \therefore $ Given determinant $ = \begin{vmatrix} 0 & 0 & 1 \\ -1 & 1 & 1 \\ -1 & 0 & 2 \\ \end{vmatrix}=1=[z] $
BETA
