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QJEEM17Ma0951: JEE Main 2017 Mathematics - Class 12 JEEM17Ma0951 Solution: If S is the set of distinct values of 'b' for which the…

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 :

Multiple Choice Options

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

Step-by-Step Verified Solution

|1111a1ab1|=0

⇒\Rightarrow 1 [a – b] – 1 [1 – a] + 1 [b – a2] = 0

⇒\Rightarrow (a - 1)2 = 0

⇒\Rightarrow a = 1

For a = 1, the equations become

x + y + z = 1

x + y + z = 1

x + by + z = 0

These equations give no solution for b = 1

⇒\Rightarrow S is singleton set.

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