If the system of equation `{:(,x-2y+z=a),(2x+y-2z=b),and,(x+3y-3z=c):}`
have at least one solution, then the relationalship between a,b,c is

Options

A. `a+b+c=0`
B. `a-b+c=0`
C. `-a+b+c=0`
D. `a+b-c=0`

Answer

B

Explanation

`(b)` `Delta=|{:(1,-2,1),(2,1,-2),(1,3,-3):}|=0`
Hence for atleast one solution
if `Delta_(1)=Delta_(2)=Delta_(3)=0`
`:.Delta_(1)=|{:(a,-2,1),(b,1,-2),(c,3,-3):}|=0`
`impliesa-b+c=0`
From `Delta_(2)=0` and `Delta_(3)=0`, we get the same condition.