1
GATE ECE 2012
+1
-0.3
Given that $$A = \left[ {\matrix{ { - 5} & { - 3} \cr 2 & 0 \cr } } \right]$$ and $${\rm I} = \left[ {\matrix{ 1 & 0 \cr 0 & 1 \cr } } \right],$$ the value of $${A^3}$$ is
A
$$15A+12$$ $${\rm I}$$
B
$$19A+30$$ $${\rm I}$$
C
$$17A+15$$ $${\rm I}$$
D
$$17A+21$$ $${\rm I}$$
2
GATE ECE 2011
+1
-0.3
The system of equations $$x+y+z=6,$$ $$x+4y+6z=20,$$ $$x + 4y + \lambda z = \mu$$ has no solution for values of $$\lambda$$ and $$\mu$$ given by
A
$$\lambda = 6,\,\,\mu = 20$$
B
$$\lambda = 6,\,\,\mu \ne 20$$
C
$$\lambda \ne 6,\,\,\mu = 20$$
D
$$\lambda \ne 6,\,\,\mu \ne 20$$
3
GATE ECE 2010
+1
-0.3
The eigen values of a skew-symmetric matrix are
A
always zero
B
always pure imaginary
C
either zero (or) pure imaginary
D
always real
4
GATE ECE 2008
+1
-0.3
All the four entries of $$2$$ $$x$$ $$2$$ matrix
$$P = \left[ {\matrix{ {{p_{11}}} & {{p_{12}}} \cr {{p_{21}}} & {{p_{22}}} \cr } } \right]$$ are non-zero and one of the eigen values is zero. Which of the following statement is true?
A
$${P_{11}}\,{P_{22}} - {P_{12}}\,{P_{21}} = 1$$
B
$${P_{11}}\,{P_{22}} - {P_{12}}\,{P_{21}} = - 1$$
C
$${P_{11}}\,{P_{22}} - {P_{21}}\,{P_{12}} = 0$$
D
$${P_{11}}\,{P_{22}} + {P_{12}}\,{P_{21}} = 0$$
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