1
GATE ECE 2014 Set 1
Numerical
+1
-0
Consider the matrix $${J_6} = \left[ {\matrix{
0 & 0 & 0 & 0 & 0 & 1 \cr
0 & 0 & 0 & 0 & 1 & 0 \cr
0 & 0 & 0 & 1 & 0 & 0 \cr
0 & 0 & 1 & 0 & 0 & 0 \cr
0 & 1 & 0 & 0 & 0 & 0 \cr
1 & 0 & 0 & 0 & 0 & 0 \cr
} } \right]$$
Which is obtained by reversing the order of the columns of the identity matrix $${{\rm I}_6}$$. Let $$P = {{\rm I}_6} + \alpha \,\,{J_6},$$ where $$\alpha $$ is a non $$-$$ negative real number. The value of $$\alpha $$ for which det $$(P)=0$$ is _______.
Your input ____
2
GATE ECE 2013
MCQ (Single Correct Answer)
+1
-0.3
The minimum eigenvalue of the following matrix is $$\left[ {\matrix{
3 & 5 & 2 \cr
5 & {12} & 7 \cr
2 & 7 & 5 \cr
} } \right]$$
3
GATE ECE 2013
MCQ (Single Correct Answer)
+1
-0.3
Let $$A$$ be an $$m\,\, \times \,\,n$$ matrix and $$B$$ an $$n\,\, \times \,\,m$$ matrix. It is given that determinant $$\left( {{{\rm I}_m} + AB} \right) = $$determinant $$\left( {{{\rm I}_n} + BA} \right),$$ where $${{{\rm I}_k}}$$ is the $$k \times k$$ identity matrix. Using the above property, the determinant of the matrix given below is $$\left[ {\matrix{
2 & 1 & 1 & 1 \cr
1 & 2 & 1 & 1 \cr
1 & 1 & 2 & 1 \cr
1 & 1 & 1 & 2 \cr
} } \right]$$
4
GATE ECE 2012
MCQ (Single Correct Answer)
+1
-0.3
Given that $$A = \left[ {\matrix{
{ - 5} & { - 3} \cr
2 & 0 \cr
} } \right]$$ and $${\rm I} = \left[ {\matrix{
1 & 0 \cr
0 & 1 \cr
} } \right],$$ the value of $${A^3}$$ is
Questions Asked from Linear Algebra (Marks 1)
Number in Brackets after Paper Indicates No. of Questions
GATE ECE 2024 (1)
GATE ECE 2023 (1)
GATE ECE 2022 (1)
GATE ECE 2018 (2)
GATE ECE 2017 Set 1 (2)
GATE ECE 2016 Set 2 (1)
GATE ECE 2016 Set 1 (1)
GATE ECE 2016 Set 3 (1)
GATE ECE 2015 Set 2 (1)
GATE ECE 2015 Set 1 (2)
GATE ECE 2015 Set 3 (1)
GATE ECE 2014 Set 3 (1)
GATE ECE 2014 Set 2 (3)
GATE ECE 2014 Set 1 (3)
GATE ECE 2013 (2)
GATE ECE 2012 (1)
GATE ECE 2011 (1)
GATE ECE 2010 (1)
GATE ECE 2008 (2)
GATE ECE 2006 (2)
GATE ECE 2000 (1)
GATE ECE 1998 (1)
GATE ECE 1994 (2)
GATE ECE Subjects
Signals and Systems
Representation of Continuous Time Signal Fourier Series Fourier Transform Continuous Time Signal Laplace Transform Discrete Time Signal Fourier Series Fourier Transform Discrete Fourier Transform and Fast Fourier Transform Discrete Time Signal Z Transform Continuous Time Linear Invariant System Discrete Time Linear Time Invariant Systems Transmission of Signal Through Continuous Time LTI Systems Sampling Transmission of Signal Through Discrete Time Lti Systems Miscellaneous
Network Theory
Control Systems
Digital Circuits
General Aptitude
Electronic Devices and VLSI
Analog Circuits
Engineering Mathematics
Microprocessors
Communications
Electromagnetics