GATE ME 2006 | Linear Algebra Question 36 | Engineering Mathematics

GATE ME 2006

MCQ (Single Correct Answer)

-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 $${S^2} = SS?$$

$$1$$ and $$25$$

$$6,4$$

$$5,1$$

$$2,10$$

GATE ME 2006

MCQ (Single Correct Answer)

-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 $$F?$$

$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr {sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$

$$\left[ {\matrix{ {\cos \theta } & {\cos \theta } & 0 \cr { - \cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$

$$\left[ {\matrix{ {\cos \theta } & { - sin\theta } & 0 \cr { - sin\theta } & {\cos \theta } & 0 \cr 0 & 0 & 1 \cr } } \right]\,$$

$$\left[ {\matrix{ {sin\theta } & { - \cos \theta } & 0 \cr {\cos \theta } & {sin\theta } & 0 \cr 0 & 0 & 1 \cr } } \right]$$

GATE ME 2005

MCQ (Single Correct Answer)

-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

$${\left[ {\matrix{ 1 & { - 2} & 0 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 0 & { 0} & 1 & 0 \cr } } \right]^T}$$

$${\left[ {\matrix{ 1 & { 0} & 0 & -2 \cr } } \right]^T}$$

$${\left[ {\matrix{ 1 & { - 1} & 2 & 1 \cr } } \right]^T}$$