From this they got lambda = 1 ,-3 .
But for these values the equations have trivial solution as determinant is zero .
Then why the they have the answer as 'contains two elements'
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Determinant zero means that there are non-trivial solutions to $Av=0$, which is what you are doing here. – Thomas Andrews Mar 31 '17 at 16:40
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Please don’t include important parts of your question as an image. It’s neither searchable nor accessible to people using screen readers. You’re much more likely to get answers to your questions that way, too. – amd Mar 31 '17 at 18:00