The matrix $A = \left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&{\frac{1}{2}}\ 0&{ - 1}&0\ {\frac{1}{2}}&0&{\frac{3}{2}} \end{array}} \right]$ 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?

Question

The matrix $A = \left[ {\begin{array}{*{20}{c}} {\frac{3}{2}}&0&{\frac{1}{2}}\ 0&{ - 1}&0\ {\frac{1}{2}}&0&{\frac{3}{2}} \end{array}} \right]$ 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?

TuteeHUB · Accepted Answer

$\left[ {\begin{array}{*{20}{c}} 1\ { - 1}\ 1 \end{array}} \right]$

TuteeHUB · Answer

$\left[ {\begin{array}{*{20}{c}} 0\ 0\ { - 1} \end{array}} \right]$

TuteeHUB · Answer

$\left[ {\begin{array}{*{20}{c}} { - 1}\ 0\ 0 \end{array}} \right]$

TuteeHUB · Answer

$\left[ {\begin{array}{*{20}{c}} 1\ 0\ { - 1} \end{array}} \right]$

1.	The matrix \(A = \left[ {\begin{array}{{20}{c}} {\frac{3}{2}}&0&{\frac{1}{2}}\\ 0&{ - 1}&0\\ {\frac{1}{2}}&0&{\frac{3}{2}} \end{array}} \right]\) 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» D. \(\left[ {\begin{array}{*{20}{c}} 1\\ { - 1}\\ 1 \end{array}} \right]\)

Discussion

No Comment Found

Related MCQs

Reply to Comment