1
GATE ECE 2014 Set 1
+1
-0.3
For matrices of same dimension $$M,N$$ and scalar $$c,$$ which one of these properties DOES NOT ALWAYS hold ?
A
$${\left( {{M^T}} \right)^T} = M$$
B
$${\left( {cM} \right)^T} = c{\left( M \right)^T}$$
C
$${\left( {M + N} \right)^T} = {M^T} + {N^T}$$
D
$$MN=NM$$
2
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 _______.

3
GATE ECE 2014 Set 1
Numerical
+1
-0
$$A$$ real $$\left( {4\,\, \times \,\,4} \right)$$ matrix $$A$$ satisfies the equation $${A^2} = {\rm I},$$ where $${\rm I}$$ is the $$\left( {4\,\, \times \,\,4} \right)$$ identity matrix. The positive eigen value of $$A$$ is _______.
4
GATE ECE 2013
+1
-0.3
The minimum eigenvalue of the following matrix is $$\left[ {\matrix{ 3 & 5 & 2 \cr 5 & {12} & 7 \cr 2 & 7 & 5 \cr } } \right]$$
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
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
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