jee-main 2015 Q63

jee-main · India · 10apr 3x3 Matrices Linear System Existence and Uniqueness via Determinant

The set of all values of $\lambda$ for which the system of linear equations: $2x_1 - 2x_2 + x_3 = \lambda x_1$ $2x_1 - 3x_2 + 2x_3 = \lambda x_2$ $-x_1 + 2x_2 = \lambda x_3$ has a non-trivial solution:
(1) is an empty set
(2) is a singleton
(3) contains two elements
(4) contains more than two elements

The set of all values of $\lambda$ for which the system of linear equations:\\
$2x_1 - 2x_2 + x_3 = \lambda x_1$\\
$2x_1 - 3x_2 + 2x_3 = \lambda x_2$\\
$-x_1 + 2x_2 = \lambda x_3$\\
has a non-trivial solution:\\
(1) is an empty set\\
(2) is a singleton\\
(3) contains two elements\\
(4) contains more than two elements

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