If [ ] denotes the greatest integer less than or equal to the real number under consideration and −1≤x<0,0≤y<1, 1≤z<2 then the value of the determinant [x]+1[y][z][x][y]+1[z][x][y][z]+1, is

If [ ] denotes the greatest integer less than or equal to the real number under consideration and −1≤x

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

Solution:

We have, [x] = -1, [y] = 0 and [z] = 1

$∴ |\begin{array}{ccc} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{array}| = |\begin{array}{rcc} 0 & 0 & 1 \\ - 1 & 1 & 1 \\ - 1 & 0 & 2 \end{array}| = 1 = [z]$

If [ ] denotes the greatest integer less than or equal to the real number under consideration and $- 1 \leq x < 0, 0 \leq y < 1$ , $1 \leq z < 2$ then the value of the determinant $|\begin{array}{ccc} [x] + 1 & [y] & [z] \\ [x] & [y] + 1 & [z] \\ [x] & [y] & [z] + 1 \end{array}|$ , is

Solution:

Related content