Matrices and Determinants Part 2

Given, A=(

[x+1]	[x+2]	[x+3]
[x]	[x+3]	[x+3]
[x]	[x+2]	[x+4]

)
A=(

[x]+1	[x]+2	[x]+3
[x]	[x]+3	[x]+3
[x]	[x]+2	[x]+4

) (∵ [x + n] = n + [x], n ∈ I)
Applying R1→R1−R3,R2→R2−R3
A=[

1	0	−1
0	1	−1
[x]	[x]+2	[x]+4

]
det(A) = 1([x] + 4 + [x] + 2) − 1(−[x])
= 3[x] + 6
∵ det(A) = 192
⇒ 3[x] + 6 = 192
⇒ [x] = 62
⇒ 62 ≤ x < 6
⇒ x ∈ [62,63)