QJEEM19Ma8d6d: JEE Main 2019 Mathematics - Class 12 JEEM19Ma8d6d Solution: The set of all values of λ for which the system of linear…

Question

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The set of all values of

λ

for which the system of linear equations
x – 2y – 2z =

λ

x
x + 2y + z =

λ

y
– x – y =

λ

z
has a non-trivial solutions :

Accepted Answer

| \begin{matrix} λ - 1 & 2 & 2 \\ 1 & 2 - λ & 1 \\ 1 & 1 & 1 \end{matrix} | = 0

\Rightarrow {(λ - 1)}^{3} = 0 \Rightarrow λ = 1

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