1
GATE ME 2006
+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
$$\left[ {\matrix{ {sin\theta } & { - \cos \theta } & 0 \cr {\cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$
2
GATE ME 2005
+2
-0.6
Which one of the following is an eigen vector of the matrix $$\left[ {\matrix{ 5 & 0 & 0 & 0 \cr 0 & 5 & 0 & 0 \cr 0 & 0 & 2 & 1 \cr 0 & 0 & 3 & 1 \cr } } \right]$$ is
A
$${\left[ {\matrix{ 1 & { - 2} & 0 & 0 \cr } } \right]^T}$$
B
$${\left[ {\matrix{ 0 & { 0} & 1 & 0 \cr } } \right]^T}$$
C
$${\left[ {\matrix{ 1 & { 0} & 0 & -2 \cr } } \right]^T}$$
D
$${\left[ {\matrix{ 1 & { - 1} & 2 & 1 \cr } } \right]^T}$$
GATE ME Subjects
EXAM MAP
Medical
NEET