1
GATE ME 2013
MCQ (Single Correct Answer)
+1
-0.3
The eigen values of a symmetric matrix are all
A
complex with non-zero positive imaginary part.
B
complex with non-zero negative imaginary part.
C
real
D
pure imaginary
2
GATE ME 2012
MCQ (Single Correct Answer)
+1
-0.3
For the matrix $$A = \left[ {\matrix{ 5 & 3 \cr 1 & 3 \cr } } \right],$$ ONE of the normalized eigen vectors is given as
A
$$\left( {\matrix{ {{1 \over 2}} \cr {{{\sqrt 3 } \over 2}} \cr } } \right)$$
B
$$\left( {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{{ - 1} \over {\sqrt 2 }}} \cr } } \right)$$
C
$$\left( {\matrix{ {{3 \over {\sqrt {10} }}} \cr {{{ - 1} \over {\sqrt {10} }}} \cr } } \right)$$
D
$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$
3
GATE ME 2011
MCQ (Single Correct Answer)
+1
-0.3
Eigen values of a real symmetric matrix are always
A
positive
B
negative
C
real
D
$$162.$$ $$\left[ {\rm A} \right]$$ is a square
4
GATE ME 2011
MCQ (Single Correct Answer)
+1
-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
a unique solution
B
no solution
C
infinite number of solutions
D
five solutions
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