1
GATE ME 2016 Set 3
Numerical
+2
-0
The number of linear independent eigenvectors of matrix $$A = \left[ {\matrix{ 2 & 1 & 0 \cr 0 & 2 & 0 \cr 0 & 0 & 3 \cr } } \right]$$ is ________.
2
GATE ME 2015 Set 3
+2
-0.6
For a given matrix $$P = \left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right],$$ where $$i = \sqrt { - 1} ,$$ the inverse of matrix $$P$$ is
A
$${1 \over {24}}\left[ {\matrix{ {4 - 3i} & i \cr { - i} & {4 + 3i} \cr } } \right]$$
B
$${1 \over {25}}\left[ {\matrix{ i & {4 - 3i} \cr {4 + 3i} & i \cr } } \right]$$
C
$${1 \over {24}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$
D
$${1 \over {25}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$
3
GATE ME 2013
+2
-0.6
Choose the CORRECT set of functions, which are linearly dependent.
A
$$\sin x,\,{\sin ^2}x$$ and $${\cos ^2}x$$
B
$$\cos x,\sin x$$ and $$\tan x$$
C
$$\cos \,2x,{\sin ^2}x$$ and $${\cos ^2}x$$
D
$$\cos \,2x,\sin x$$ and $$\cos x$$
4
GATE ME 2012
+2
-0.6
$$x+2y+z=4, 2x+y+2z=5, x-y+z=1$$
The system of algebraic equations given above has
A
a unique solution of $$x=1,y=1$$ and $$z=1$$
B
only the two solutions of $$x=1, y=1, z=1$$ and $$x=2, y=1, z=0$$
C
infinite number of solutions.
D
no feasible solution.
GATE ME Subjects
Engineering Mechanics
Strength of Materials
Theory of Machines
Engineering Mathematics
Machine Design
Fluid Mechanics
Turbo Machinery
Heat Transfer
Thermodynamics
Production Engineering
Industrial Engineering
General Aptitude
EXAM MAP
Joint Entrance Examination