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The eigen values and the corresponding eigen vectors of a 2...

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Linear Algebra
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The eigen values and the corresponding eigen vectors of a 2 × 2 matrix are given by
\[\begin{array}{*{20}{c}} {{\text{Eigen value}}}&{{\text{Eigen vector}}} \\ {{\lambda _1} = 8}&{{{\text{v}}_1} = \left[ {\begin{array}{*{20}{c}} 1 \\ 1 \end{array}} \right]} \\ {{\lambda _2} = 4}&{{{\text{v}}_2} = \left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \end{array}} \right]} \end{array}\]
The matrix is

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Correct Answer: Option A
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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
A. 1 B. 2 C. 3 D. 5
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