1
GATE ECE 2016 Set 2
Numerical
+1
-0
The value of $$x$$ for which the matrix $$A = \left[ {\matrix{ 3 & 2 & 4 \cr 9 & 7 & {13} \cr { - 6} & { - 4} & { - 9 + x} \cr } } \right]$$ has zero as an eigen value is __________.
Your input ____
2
GATE ECE 2016 Set 3
MCQ (Single Correct Answer)
+1
-0.3
Consider a $$2 \times 2$$ square matrix $$A = \left[ {\matrix{ \sigma & x \cr \omega & \sigma \cr } } \right]$$
Where $$x$$ is unknown. If the eigenvalues of the matrix $$A$$ are $$\left( {\sigma + j\omega } \right)$$ and $$\left( {\sigma - j\omega } \right)$$, then $$x$$ is equal to
A
$$+ j\omega$$
B
$$- j\omega$$
C
$$+ \omega$$
D
$$- \omega$$
3
GATE ECE 2016 Set 1
MCQ (Single Correct Answer)
+1
-0.3
Let $${M^4} = {\rm I}$$ (where $${\rm I}$$ denotes the identity matrix) and $$M \ne {\rm I},\,\,{M^2} \ne {\rm I}$$ and $${M^3} \ne {\rm I}$$. Then, for any natural number $$k,$$ $${M^{ - 1}}$$ equals:
A
$${M^{4k + 1}}$$
B
$${M^{4k + 2}}$$
C
$${M^{4k + 3}}$$
D
$${M^{4k}}$$
4
GATE ECE 2015 Set 2
MCQ (Single Correct Answer)
+1
-0.3
The value of $$'x'$$ for which all the eigenvalues of the matrix given below are real is $$\left[ {\matrix{ {10} & {5 + j} & 4 \cr x & {20} & 2 \cr 4 & 2 & { - 10} \cr } } \right]$$
A
$$5+j$$
B
$$5-j$$
C
$$1-5j$$
D
$$1+5j$$
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