Set, Relation and FunctionHard
Question
If 0 ≤ [x] < 2 , - 1 ≤ [y] < 1 and 1 ≤ [z] < 3 where [·] denotes the greatest integer function, then the maximum value of the determinant 
is
isOptions
A.2
B.4
C.6
D.8
Solution
∵ 0 ≤ [x] < 2 ⇒ [x] = 0 , 1
- 1 ≤ [y] < 1 ⇒ [y] = - 1, 0
1 ≤ [z] < 3 ⇒ [z] = 1 ; 2
Now apply R2 → R2 - R1, R3 → R3 - R1
= [x] + [y] + [z] + 1
= 1 + 0 + 2 + 1 = 4 (Max. value)
- 1 ≤ [y] < 1 ⇒ [y] = - 1, 0
1 ≤ [z] < 3 ⇒ [z] = 1 ; 2
Now apply R2 → R2 - R1, R3 → R3 - R1
= [x] + [y] + [z] + 1= 1 + 0 + 2 + 1 = 4 (Max. value)
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