1
GATE IN 2014
MCQ (Single Correct Answer)
+1
-0.3
For the matrix $$A$$ satisfying the equation given below, the eigen values are $$\left[ A \right]\left[ {\matrix{ 1 & 2 & 3 \cr 7 & 8 & 9 \cr 4 & 5 & 6 \cr } } \right] = \left[ {\matrix{ 1 & 2 & 3 \cr 4 & 5 & 6 \cr 7 & 8 & 9 \cr } } \right]$$\$
A
$$(1,-j,j)$$
B
$$(1,1,0)$$
C
$$(1,1,-1)$$
D
$$(1,0,0)$$
2
GATE IN 2013
MCQ (Single Correct Answer)
+1
-0.3
The dimension of the null space of the matrix $$\left[ {\matrix{ 0 & 1 & 1 \cr 1 & { - 1} & 0 \cr { - 1} & 0 & { - 1} \cr } } \right]$$ is
A
$$0$$
B
$$1$$
C
$$2$$
D
$$3$$
3
GATE IN 2012
MCQ (Single Correct Answer)
+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
$$17A+21$$ $${\rm I}$$
4
GATE IN 2011
MCQ (Single Correct Answer)
+1
-0.3
The matrix $$M = \left[ {\matrix{ { - 2} & 2 & { - 3} \cr 2 & 1 & 6 \cr { - 1} & { - 2} & 0 \cr } } \right]$$ has eigen values $$-3, -3, 5.$$ An eigen vector corresponding to the eigen value $$5$$ is $${\left[ {\matrix{ 1 & 2 & { - 1} \cr } } \right]^T}.$$ One of the eigen vector of the matrix $${M^3}$$ is
A
$${\left[ {\matrix{ 1 & 8 & { - 1} \cr } } \right]^T}$$
B
$${\left[ {\matrix{ 1 & 2 & { - 1} \cr } } \right]^T}$$
C
$${\left[ {\matrix{ 1 & {\root 3 \of 2 } & { - 1} \cr } } \right]^T}$$
D
$${\left[ {\matrix{ 1 & 1 & { - 1} \cr } } \right]^T}$$
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