1
GATE ECE 2005
+2
-0.6
Given an orthogonal matrix $$A = \left[ {\matrix{ 1 & 1 & 1 & 1 \cr 1 & 1 & { - 1} & { - 1} \cr 1 & { - 1} & 0 & 0 \cr 0 & 0 & 1 & { - 1} \cr } } \right]$$ then the value of $${\left( {A{A^T}} \right)^{ - 1}}$$ is
A
$${1 \over 4}{{\rm I}_4}$$
B
$${1 \over 2}{{\rm I}_4}$$
C
$${\rm I}$$
D
$${1 \over 3}{{\rm I}_4}$$
2
GATE ECE 2005
+2
-0.6
Given the matrix $$\left[ {\matrix{ { - 4} & 2 \cr 4 & 3 \cr } } \right],$$ the eigen vector is
A
$$\left[ {\matrix{ 3 \cr 2 \cr } } \right]$$
B
$$\left[ {\matrix{ 4 \cr 3 \cr } } \right]$$
C
$$\left[ {\matrix{ 2 \cr { - 1} \cr } } \right]$$
D
$$\left[ {\matrix{ { - 2} \cr 1 \cr } } \right]$$
3
GATE ECE 2005
+2
-0.6
If $$A = \left[ {\matrix{ 2 & { - 0.1} \cr 0 & 3 \cr } } \right]$$ and $${A^{ - 1}} = \left[ {\matrix{ {{\raise0.5ex\hbox{\scriptstyle 1} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{\scriptstyle 2}}} & a \cr 0 & b \cr } } \right]$$ then $$a+b=$$
A
$${7 \over {20}}$$
B
$${3 \over {20}}$$
C
$${19 \over {60}}$$
D
$${11 \over {20}}$$
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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