The value of \( \lambda \) for which the system of equations \[ \be...

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The value of \( \lambda \) for which the system of equations
\[
\begin{array}{l}
(1+\lambda) x_{1}+x_{2}+x_{3}=1 \\
x_{1}+(1+\lambda) x_{2}+x_{3}=1 \\
x_{1}+x_{2}+(1+\lambda) x_{3}=1
\end{array}
\]
has infinitely many solutions.
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