1
GATE EE 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 EE 2010
+1
-0.3
An eigen vector of $$p = \left[ {\matrix{ 1 & 1 & 0 \cr 0 & 2 & 2 \cr 0 & 0 & 3 \cr } } \right]$$ is
A
$${\left[ {\matrix{ { - 1} & 1 & 1 \cr } } \right]^T}$$
B
$${\left[ {\matrix{ { 1} & 2 & 1 \cr } } \right]^T}$$
C
$${\left[ {\matrix{ { 1} & - 1 & 2 \cr } } \right]^T}$$
D
$${\left[ {\matrix{ { 2} & 1 & -1 \cr } } \right]^T}$$
3
GATE EE 2009
+1
-0.3
The trace and determinant of a $$2 \times 2$$ matrix are shown to be $$-2$$ and $$-35$$ respectively. Its eigen values are
A
$$-30, -5$$
B
$$-37,-1$$
C
$$-7,5$$
D
$$17.5, -2$$
4
GATE EE 2008
+1
-0.3
The characteristic equation of a $$3\,\, \times \,\,3$$ matrix $$P$$ is defined as
$$\alpha \left( \lambda \right) = \left| {\lambda {\rm I} - P} \right| = {\lambda ^3} + 2\lambda + {\lambda ^2} + 1 = 0.$$
If $${\rm I}$$ denotes identity matrix then the inverse of $$P$$ will be
A
$${P^2} + P + 2{\rm I}$$
B
$${P^2} + P + {\rm I}$$
C
$$- \left( {{P^2} + P + {\rm I}} \right)$$
D
$$- \left( {{P^2} + P + 2{\rm I}} \right)$$
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