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Engineering Maths · Q91

Linear Algebra

Engineering and GATE · Engineering Maths · question 91

Q91

The matrix \[ A = [ array*20c 3/2&0&1/2 \\ 0& - 1&0 \\ 1/2&0&3/2 array ]\] has three distinct eigen values and one of its eigen vectors is \[ [ array*20c 1 \\ 0 \\ 1 array ].\] Which one of the following can be another eigen vector of A?

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]
Answer
D.
\left[ {\begin{array}{*{20}{c}} 1 \\ { - 1} \\ 1 \end{array}} \right]

Answer: Option C

Solution

Answer: Option C
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