If `S` is the set of distinct values of `' b` for which the following system of linear equations `x+y+z=1` `x+a y+z=1` `a x+b y+z=0` has no solution, then `S` is : a finite set containing two or more elements (2) a singleton an empty set (4) an infinite set

Options

A. a singleton set
B. an empty set
C. an infinite set
D. a finite set containing two or more elements

Answer

1

Explanation

Since system of equations has no solutions
`Delta = |{:(1,,1,,1),(1,,a,,1),(a,,b,,1):}|=0`
` rArr a=1`
Also at a=1 `,Delta_(1) = Delta_(2) =Delta_(3)=0`
But when a=1 and b=1 system of equation becomes
`x+y+z=1`
` " and " x+y+z=0`
This system has no solution
`:. b= {1}`