11. For the matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
3&{ - 2}&2 \\
0&{ - 2}&1 \\
0&0&1
\end{array}} \right],\] one of the eigen values is equal to -2. Which of the following is an eigen vector?
12. What are the eigen values of the following 2 × 2 matrix?
\[\left[ {\begin{array}{*{20}{c}}
2&{ - 1} \\
{ - 4}&5
\end{array}} \right]\]
\[\left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ { - 4}&5 \end{array}} \right]\]
13. Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}}
3&{ - 1}&{ - 1} \\
{ - 1}&3&{ - 1} \\
{ - 1}&{ - 1}&3
\end{array}} \right]\] are
14. If \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&5 \\
6&2
\end{array}} \right]\] and \[{\text{B}} = \left[ {\begin{array}{*{20}{c}}
3&7 \\
8&4
\end{array}} \right],\,{\text{A}}{{\text{B}}^{\text{T}}}\] is equal to
15. The number of linearly independent eigen vectors of \[\left[ {\begin{array}{*{20}{c}}
2&1 \\
0&2
\end{array}} \right]\] is
16. A 3 × 3 matrix P is such that, P3 = P. Then the eigen values of P are
17. One of the eigen vectors of matrix is \[\left[ {\begin{array}{*{20}{c}}
{ - 5}&2 \\
{ - 9}&6
\end{array}} \right]\] is
18. For the matrix \[\left[ {\begin{array}{*{20}{c}}
4&2 \\
2&4
\end{array}} \right]\] the eigen value corresponding to the eigen vector \[\left[ {\begin{array}{*{20}{c}}
{101} \\
{101}
\end{array}} \right]\] is
19. The eigen values of matrix \[\left[ {\begin{array}{*{20}{c}}
9&5 \\
5&8
\end{array}} \right]\] are
20. Consider the 5 × 5 matrix \[{\text{A}} = \left[ {\begin{array}{*{20}{c}}
1&2&3&4&5 \\
5&1&2&3&4 \\
4&5&1&2&3 \\
3&4&5&1&2 \\
2&3&4&5&1
\end{array}} \right]\]
It is given that A has only one real eigen value.
Then the real eigen value of A is
It is given that A has only one real eigen value.
Then the real eigen value of A is
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