1
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
$${1 \over {25}}\left[ {\matrix{ {4 + 3i} & { - i} \cr i & {4 - 3i} \cr } } \right]$$
2
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 $$\cos x$$
3
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.
4
GATE ME 2008
+2
-0.6
The eigen vectors of the matrix $$\left[ {\matrix{ 1 & 2 \cr 0 & 2 \cr } } \right]$$ are written in the form $$\left[ {\matrix{ 1 \cr a \cr } } \right]\,\,\& \,\,\left[ {\matrix{ 1 \cr b \cr } } \right].$$ What is $$a+b$$?
A
$$0$$
B
$${1 \over 2}$$
C
$$1$$
D
$$2$$
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