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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?
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Answer: Option D
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12
What are the eigen values of the following 2 × 2 matrix?
\[\left[ {\begin{array}{*{20}{c}} 2&{ - 1} \\ { - 4}&5 \end{array}} \right]\]
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Answer: Option B
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13
Eigen values of the matrix \[\left[ {\begin{array}{*{20}{c}} 3&{ - 1}&{ - 1} \\ { - 1}&3&{ - 1} \\ { - 1}&{ - 1}&3 \end{array}} \right]\]   are
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Answer: Option C
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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
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Answer: Option A
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15
The number of linearly independent eigen vectors of \[\left[ {\begin{array}{*{20}{c}} 2&1 \\ 0&2 \end{array}} \right]\]  is
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Answer: Option B
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16
A 3 × 3 matrix P is such that, P3 = P. Then the eigen values of P are
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Answer: Option D
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17
One of the eigen vectors of matrix is \[\left[ {\begin{array}{*{20}{c}} { - 5}&2 \\ { - 9}&6 \end{array}} \right]\]  is
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Answer: Option D
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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
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Answer: Option C
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19
The eigen values of matrix \[\left[ {\begin{array}{*{20}{c}} 9&5 \\ 5&8 \end{array}} \right]\] are
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Answer: Option B
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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
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Answer: Option C
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