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The set of all values of lambda for ...

The set of all values of `lambda` for which the system of linear equations : `2x_1-2x_2+""x_3=lambdax_1` `2x_1-3x_2+""2x_3=lambdax_2` `-x_1+""2x_2=lambdax_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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To determine the set of all values of \( \lambda \) for which the given system of linear equations has a non-trivial solution, we need to analyze the system and find the determinant of the coefficient matrix. If the determinant is zero, the system has either no solutions or infinitely many solutions (the latter indicating a non-trivial solution). The given equations are: 1. \( 2x_1 - 2x_2 + x_3 = \lambda x_1 \) 2. \( 2x_1 - 3x_2 + 2x_3 = \lambda x_2 \) 3. \( -x_1 + 2x_2 = \lambda x_3 \) ...
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