The solutiion of `(x,y,z)` the equation `[(-1,0,1),(-1,1,0),(0,-1,1)][(x),(y),(z)]=[(1),(1),(2)]` is `(x,y,z)`

Options

A. (1,1,1)
B. (0,-1,2)
C. (-1,2,2)
D. (-1, 0, 2)

Answer

D

Explanation

`[{:(1,0,1),(-1,1,0),(0,-1,1):}][{:(x),(y),(z):}]=[{:(1),(1),(2):}]`
`[{:(x,+0y,z),(-x,1,0z),(0x,-y,+z):}]=[{:(1),(1),(2):}]`
`rArr x+z=1`
`-x+y=1`
and `-y+z=2`
On solving these equations, we get
`x=-1,y=0,z=2`