jee-main 2016 Q66

jee-main · India · 09apr Matrices Linear System and Inverse Existence

The system of linear equations \begin{align*} x + \lambda y - z &= 0 \lambda x - y - z &= 0 x + y - \lambda z &= 0 \end{align*} has a non-trivial solution for:
(1) infinitely many values of $\lambda$
(2) exactly one value of $\lambda$
(3) exactly two values of $\lambda$
(4) exactly three values of $\lambda$

The system of linear equations
\begin{align*}
x + \lambda y - z &= 0\\
\lambda x - y - z &= 0\\
x + y - \lambda z &= 0
\end{align*}
has a non-trivial solution for:\\
(1) infinitely many values of $\lambda$\\
(2) exactly one value of $\lambda$\\
(3) exactly two values of $\lambda$\\
(4) exactly three values of $\lambda$

Paper Questions

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