JEE Main Solved Paper 2017 Question 5
Question: 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 Main Solved Paper-2017]
Options:
A) a singleton
B) an empty set
C) an infinite set
D) a finite set containing two or more elements
Show Answer
Answer:
Correct Answer: A
Solution:
$ D= \begin{matrix} 1 & 1 & 1 \\ 1 & a & 1 \\ a & b & 1 \\ \end{matrix} =0\Rightarrow a=1 $ and at $ a=1 $ $ D _1=D _2=D _3=0 $
$ \begin{matrix} First two equations are \\ and third equation is \\ \end{matrix}. \begin{matrix} x+y+z=1 \\ x+y+z=0 \\ \end{matrix} \Rightarrow There is no solution $
$ \therefore $ $ b={1}\Rightarrow $ it is a singleton set
