#### If S is the set of distinct values of ‘b’ for which the following system of linear equationsx+y+z=1x+ay+z=1ax+by+z=0has no solution, then S is : Option 1)  an infinite set   Option 2)  a finite set containing two or more elements   Option 3) a singleton   Option 4)  an empty set

As we leant in

Cramer's rule for solving system of linear equations -

When   and  ,

then  the system of equations has infinite solutions.

- wherein

and

are obtained by replacing column 1,2,3 of  by   column

= 1 (a -b) - 1(1 -a) + 1 (b - a2) = 0

=a - b - 1 + a + b - a2 = 0

=> 2a - 1 -a=0

=> a2- 2a +1 =0

=> (a - 1)= 0

=> a = 1

It is independent of b

Option 1)

an infinite set

Incorrect

Option 2)

a finite set containing two or more elements

Incorrect

Option 3)

a singleton

Correct

Option 4)

an empty set

Incorrect