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## If S is the set of distinct values of b for which the following system of linear equations x + y + z = 1 x + ay + z = 1 ax + by + z = 0 has no solution, then S is :-JEE MAINS-Mathematics-2017

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AnswersAs 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 -a2 =0

=> a2- 2a +1 =0

=> (a - 1)2 = 0

=> a = 1

It is independent of b

Hence ,option 1 is correct

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