GATE ME 2012 | Linear Algebra Question 26 | Engineering Mathematics

GATE ME 2012

MCQ (Single Correct Answer)

-0.3

For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as

$$\left( {\matrix{ {{1 \over 2}} \cr {{{\sqrt 3 } \over 2}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{{ - 1} \over {\sqrt 2 }}} \cr } } \right)$$

$$\left( {\matrix{ {{3 \over {\sqrt {10} }}} \cr {{{ - 1} \over {\sqrt {10} }}} \cr } } \right)$$

$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Eigen values of a real symmetric matrix are always

positive

negative

real

$$162.$$ $$\left[ {\rm A} \right]$$ is a square

GATE ME 2011

MCQ (Single Correct Answer)

-0.3

Consider the following system of equations
$$2{x_1} + {x_2} + {x_3} = 0,\,\,{x_2} - {x_3} = 0$$ and $${x_1} + {x_2} = 0.$$
This system has

a unique solution

no solution

infinite number of solutions

five solutions

GATE ME 2010

MCQ (Single Correct Answer)

-0.3

One of the eigen vector of the matrix $$A = \left[ {\matrix{ 2 & 2 \cr 1 & 3 \cr } } \right]$$ is

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

$$\left[ {\matrix{ 2 \cr 1 \cr } } \right]$$

$$\left[ {\matrix{ 4 \cr 1 \cr } } \right]$$

$$\left[ {\matrix{ 1 \cr { - 1} \cr } } \right]$$

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