1
GATE ECE 2023
MCQ (Single Correct Answer)
+2
-0.67
The state equation of a second order system is
$$x(t) = Ax(t),\,\,\,\,x(0)$$ is the initial condition.
Suppose $$\lambda_1$$ and $$\lambda_2$$ are two distinct eigenvalues of A and $$v_1$$ and $$v_2$$ are the corresponding eigenvectors. For constants $$\alpha_1$$ and $$\alpha_2$$, the solution, $$x(t)$$, of the state equation is
2
GATE ECE 2022
MCQ (Single Correct Answer)
+2
-0.67
Let $$\alpha$$, $$\beta$$ two non-zero real numbers and v1, v2 be two non-zero real vectors of size 3 $$\times$$ 1. Suppose that v1 and v2 satisfy $$v_1^T{v_2} = 0$$, $$v_1^T{v_1} = 1$$ and $$v_2^T{v_2} = 1$$. Let A be the 3 $$\times$$ 3 matrix given by :
A = $$\alpha$$v1$$v_1^T$$ + $$\beta$$v2$$v_2^T$$
The eigen values of A are __________.
3
GATE ECE 2017 Set 2
Numerical
+2
-0
The rank of the matrix $$\left[ {\matrix{
1 & { - 1} & 0 & 0 & 0 \cr
0 & 0 & 1 & { - 1} & 0 \cr
0 & 1 & { - 1} & 0 & 0 \cr
{ - 1} & 0 & 0 & 0 & 1 \cr
0 & 0 & 0 & 1 & { - 1} \cr
} } \right]$$ is __________.
Your input ____
4
GATE ECE 2016 Set 2
Numerical
+2
-0
The matrix $$A = \left[ {\matrix{
a & 0 & 3 & 7 \cr
2 & 5 & 1 & 3 \cr
0 & 0 & 2 & 4 \cr
0 & 0 & 0 & b \cr
} } \right]$$ has det
$$(A)=100$$ and trace $$(A)=14.$$ The value of $$\left| {a - b} \right|$$ is ___________.
$$(A)=100$$ and trace $$(A)=14.$$ The value of $$\left| {a - b} \right|$$ is ___________.
Your input ____
Questions Asked from Linear Algebra (Marks 2)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Discrete Time Signal Fourier Series Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Transmission of Signal Through Continuous Time LTI Systems Discrete Time Linear Time Invariant Systems Sampling Continuous Time Signal Laplace Transform Discrete Fourier Transform and Fast Fourier Transform Transmission of Signal Through Discrete Time Lti Systems Miscellaneous Fourier Transform
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics