The system of equations `-2x+y+z=a` `x-2y+z=b` `x+y-2z=c` has

Options

A. no solution if `a+b+c ne 0`
B. unique solution if `a+b+c =0`
C. infinite number of solutions if `a+b+c=0`
D. None of these

Answer

A, C

Explanation

`Delta =|{:(-2,,1,,1),(1,,-2,,1),(1,,1,,-2):}|=0`
`Delta_(x)= |{:(a,,1,,1),(b,,-2,,1),(c,,1,,-2):}|=3a +3b+3c`
`Delta_(y) =|{:(-2,,a,,1),(1,,b,,1),(1,,1,,c):}|=3a+3b+3c`
`Delta_(z)= |{:(-2,,1,,a),(1,,-2,,b),(1,,1,,c):}|=3a+3b+3c`