1
GATE EE 2015 Set 1
+2
-0.6
The maximum value of $$'a'$$ such that the matrix $$\left[ {\matrix{ { - 3} & 0 & { - 2} \cr 1 & { - 1} & 0 \cr 0 & a & { - 2} \cr } } \right]$$ has three linearly independent real eigenvectors is
A
$${2 \over {3\sqrt 3 }}$$
B
$${1 \over {3\sqrt 3 }}$$
C
$${{1 + 2\sqrt 3 } \over {3\sqrt 3 }}$$
D
$${{1 + \sqrt 3 } \over {3\sqrt 3 }}$$
2
GATE EE 2014 Set 3
+2
-0.6
$$A = \left[ {\matrix{ p & q \cr r & s \cr } } \right];B = \left[ {\matrix{ {{p^2} + {q^2}} & {pr + qs} \cr {pr + qs} & {{r^2} + {s^2}} \cr } } \right]$$
If the rank of matrix $$A$$ is $$N$$, then the rank of matrix $$B$$ is
A
$$N/2$$
B
$$N-1$$
C
$$N$$
D
$$2$$ $$N$$
3
GATE EE 2014 Set 1
Numerical
+2
-0
A system matrix is given as follows $$A = \left[ {\matrix{ 0 & 1 & { - 1} \cr { - 6} & { - 11} & 6 \cr { - 6} & { - 11} & 5 \cr } } \right].$$\$

The absolute value of the ratio of the maximum eigenvalue to the minimum eigenvalue is ___________.

4
GATE EE 2013
+2
-0.6
The equation $$\left[ {\matrix{ 2 & { - 2} \cr 1 & { - 1} \cr } } \right]\left[ {\matrix{ {{x_1}} \cr {{x_2}} \cr } } \right] = \left[ {\matrix{ 0 \cr 0 \cr } } \right]$$ has
A
no solution
B
only one solution
C
non-zero unique solution
D
multiple solutions
GATE EE Subjects
Electric Circuits
Electromagnetic Fields
Signals and Systems
Electrical Machines
Engineering Mathematics
General Aptitude
Power System Analysis
Electrical and Electronics Measurement
Analog Electronics
Control Systems
Power Electronics
Digital Electronics
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