The set of all values of $\lambda $ for which the system of linear equations: $$\matrix{ {2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}} \cr {2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}} \cr { - {x_1} + 2{x_2} = \lambda {x_3}} \cr } $$ has a non-trivial solution

Question

The set of all values of $\lambda $ for which the system of linear equations:

$$\matrix{ {2{x_1} - 2{x_2} + {x_3} = \lambda {x_1}} \cr {2{x_1} - 3{x_2} + 2{x_3} = \lambda {x_2}} \cr { - {x_1} + 2{x_2} = \lambda {x_3}} \cr } $$

has a non-trivial solution

contains two elements

contains more than two elements

in an empty set

is a singleton

Solution

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