1
GATE EE 2007
+2
-0.6
The matrix $$A$$ given below is the node incidence matrix of a network. The columns correspond to braches of the network while the rows correspond to nodes. Let
$$V = {\left[ {{v_1}\,\,{v_2}....{v_6}} \right]^T}$$ denote the vector of branches voltages while
$${\rm I} = {\left[ {{i_1}\,{i_2}....{i_6}} \right]^T}$$ that of branch currents. The vector $$E = {\left[ {{e_1}\,{e_2}\,\,{e_3}\,{e_4}} \right]^T}$$ denotes the vector of node voltages relative to a common ground. $$A = \left[ {\matrix{ 1 & 1 & 1 & 0 & 0 & 0 \cr 0 & { - 1} & 0 & { - 1} & 1 & 0 \cr { - 1} & 0 & 0 & 0 & { - 1} & { - 1} \cr 0 & 0 & { - 1} & 1 & 0 & 1 \cr } } \right]$$\$

Which of the following statements is true?

A
The equations $${v_1} - {v_2} + {v_3} = 0,$$ $${v_3} + {v_4} - {v_5} = 0$$ are $$KVL$$ equations for the network for some loops
B
The equations $${v_1} - {v_3} - {v_6} = 0,\,$$ $${v_4} + {v_5} - {v_6} = 0$$ are $$KVL$$ equations for the network for some loops
C
$$E=AV$$
D
$$AV=0$$ are $$KVL$$ equations for the network
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