The matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
{\frac{3}{2}}&0&{\frac{1}{2}} \\
0&{ - 1}&0 \\
{\frac{1}{2}}&0&{\frac{3}{2}}
\end{array}} \right]\] has three distinct eigen values and one of its eigen vectors is \[\left[ {\begin{array}{*{20}{c}}
1 \\
0 \\
1
\end{array}} \right].\]
Which one of the following can be another eigen vector of A?
A. \[\left[ {\begin{array}{*{20}{c}} 0 \\ 0 \\ { - 1} \end{array}} \right]\]
B. \[\left[ {\begin{array}{*{20}{c}} { - 1} \\ 0 \\ 0 \end{array}} \right]\]
C. \[\left[ {\begin{array}{*{20}{c}} 1 \\ 0 \\ { - 1} \end{array}} \right]\]
D. \[\left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \\ 1 \end{array}} \right]\]
Answer: Option C
This Question Belongs to Engineering Maths >> Linear Algebra
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