1
GATE ECE 2015 Set 2
+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
$$1+5j$$
2
GATE ECE 2015 Set 1
Numerical
+1
-0
Consider system of linear equations : $$x-2y+3z=-1$$$$$x-3y+4z=1$$$ and $$-2x+4y-6z=k,$$\$

The value of $$'k'$$ for which the system has infinitely many solutions is _______.

3
GATE ECE 2015 Set 1
Numerical
+1
-0
The value of $$'P'$$ such that the vector $$\left[ {\matrix{ 1 \cr 2 \cr 3 \cr } } \right]$$ is an eigenvector of the matrix $$\left[ {\matrix{ 4 & 1 & 2 \cr P & 2 & 1 \cr {14} & { - 4} & {10} \cr } } \right]$$ is ________.
4
GATE ECE 2014 Set 3
+1
-0.3
Which one of the following statements is NOT true for a square matrix $$A$$?
A
If $$A$$ is upper triangular, the eigenvalues of $$A$$ are the diagonal elements of it
B
If $$A$$ is real symmetric, the eigenvalues of $$A$$ are always real and positive
C
If $$A$$ is real , the eigenvalues of $$A$$ and $${A^T}$$ are always the same
D
If all the principal minors of $$A$$ are positive , all the eigenvalues of $$A$$ are also positive
GATE ECE Subjects
Signals and Systems
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics
EXAM MAP
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