1
GATE ME 2012
MCQ (Single Correct Answer)
+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.
2
GATE ME 2008
MCQ (Single Correct Answer)
+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
$$2$$
3
GATE ME 2006
MCQ (Single Correct Answer)
+2
-0.6
Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$
A
$$1$$ and $$25$$
B
$$6,4$$
C
$$5,1$$
D
$$2,10$$
4
GATE ME 2006
MCQ (Single Correct Answer)
+2
-0.6
Multiplication of matrices $$E$$ and $$F$$ is $$G.$$ Matrices $$E$$ and $$G$$ are
$$E = \left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$ and $$G = \left[ {\matrix{ 1 & 0 & 0 \cr 0 & 1 & 0 \cr 0 & 0 & 1 \cr } } \right]$$
What is the matrix $$F?$$
A
$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$
B
$$\left[ {\matrix{ {\cos \theta } & {\cos \theta } & 0 \cr { - \cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$
C
$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr { - sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$
D
$$\left[ {\matrix{ {sin\theta } & { - \cos \theta } & 0 \cr {\cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$
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