1
GATE ME 2014 Set 1
+1
-0.3
Given that the determinant of the matrix $$\left[ {\matrix{ 1 & 3 & 0 \cr 2 & 6 & 4 \cr { - 1} & 0 & 2 \cr } } \right]$$ is $$-12$$, the determinant of the matrix $$\left[ {\matrix{ 2 & 6 & 0 \cr 4 & {12} & 8 \cr { - 2} & 0 & 4 \cr } } \right]$$ is
A
$$-96$$
B
$$-24$$
C
$$24$$
D
$$96$$
2
GATE ME 2014 Set 1
+1
-0.3
Which one of the following describes the relationship among the three vectors, $$\widehat i + \widehat j + \widehat k,\,\,2\widehat i + 3\widehat j + \widehat k$$ and $$5\widehat i + 6\widehat j + 4\widehat k?$$
A
The vectors are mutually perpendicular
B
The vectors are linearly dependent
C
The vectors are linearly independent
D
The vectors are unit vectors
3
GATE ME 2013
+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
4
GATE ME 2012
+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
$$\left( {\matrix{ {{1 \over 5}} \cr {{2 \over {\sqrt 5 }}} \cr } } \right)$$
GATE ME Subjects
EXAM MAP
Medical
NEET