1
GATE EE 2017 Set 1
+1
-0.3
The matrix $$A = \left[ {\matrix{ {{3 \over 2}} & 0 & {{1 \over 2}} \cr 0 & { - 1} & 0 \cr {{1 \over 2}} & 0 & {{3 \over 2}} \cr } } \right]$$ has three distinct eigen values and one of its eigen vectors is $$\left[ {\matrix{ 1 \cr 0 \cr 1 \cr } } \right].$$ Which one of the following can be another eigen vector of $$A$$?
A
$$\left[ {\matrix{ 0 \cr 0 \cr { - 1} \cr } } \right]$$
B
$$\left[ {\matrix{ { - 1} \cr 0 \cr 0 \cr } } \right]$$
C
$$\left[ {\matrix{ 1 \cr 0 \cr { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ 1 \cr { - 1} \cr 1 \cr } } \right]$$
2
GATE EE 2016 Set 2
+1
-0.3
$$A$$ $$3 \times 3$$ matrix $$P$$ is such that , $${p^3} = P.$$ Then the eigen values of $$P$$ are
A
$$1,1,-1$$
B
$$1,0.5+j0.866,0.5-j0.866$$
C
$$1,-0.5+j0.866,-05-j0.866$$
D
$$0,1,-1$$
3
GATE EE 2016 Set 1
Numerical
+1
-0
Consider $$3 \times 3$$ matrix with every element being equal to $$1.$$ Its only non-zero eigenvalue is __________.
4
GATE EE 2015 Set 2
+1
-0.3
We have a set of $$3$$ linear equations in $$3$$ unknown. $$'X \equiv Y'$$ means $$X$$ and $$Y$$ are equivalent statements and $$'X \ne Y'$$ means $$X$$ and $$y$$ are not equivalent statements.

$$P:$$ There is a unique solution.
$$Q:$$ The equations are linearly independent .
$$R:$$ All eigen values of the coefficient matrix are non zero .
$$S:$$ The determinant of the coefficient matrix is non-zero .

Which one of the following is TRUE?
A
$$P \equiv Q \equiv R \equiv S$$
B
$$P \equiv R \ne Q \equiv S$$
C
$$P \equiv Q \ne R \equiv S$$
D
$$P \ne Q \ne R \ne S$$
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