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Let text P = left begin array 20 c 3&1 1&3...

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Linear Algebra
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Let \[{\text{P}} = \left[ {\begin{array}{*{20}{c}} 3&1 \\ 1&3 \end{array}} \right].\]   Consider the set S of all vectors \[\left( {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \end{array}} \right)\] such that a2 + b2 = 1 where \[\left( {\begin{array}{*{20}{c}} {\text{a}} \\ {\text{b}} \end{array}} \right) = {\text{P}}\left( {\begin{array}{*{20}{c}} {\text{x}} \\ {\text{y}} \end{array}} \right).\]   Then S is

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Correct Answer: Option D
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If $${\left[ {1,\,0,\, - 1} \right]^{\text{T}}}$$  is an eigen vector of the following matrix \[\left[ {\begin{array}{*{20}{c}} 1&{ - 1}&0 \\ { - 1}&2&{ - 1} \\ 0&{ - 1}&1 \end{array}} \right]\]   then corresponding eigen value is
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