Let S be the set of all real values of k for which the systemof linear equations x + y + z = 2 2x + y $$-$$ z = 3 3x + 2y + kz = 4 has a unique solution. Then S is :
JEE · Math · previous-year question
- A.an empty set
- B.equal to {0}
- C.equal to R
- D.equal to R $$-$$ {0}correct
Answer
D. equal to R $$-$$ {0}
Explanation
As system of linear equations have unique solutions so, determinant of coefficient $$ \ne $$ 0 $$ \therefore $$ $$\left| {\begin{matrix} 1 & 1 & 1 \\ 2 & 1 & { - 1} \\ 3 & 2 & k \\ \end{matrix} } \right|$$ $$ \ne $$ 0 $$ \Rightarrow $$ k + 2 - (2k + 3) + 1 $$ \ne $$ 0 $$ \Rightarrow $$ k $$ \ne $$ 0 $$ \therefore $$ k $$ \in $$ R - {0}
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