The matrix A given below is the node incidence matrix of a network. The

columns correspond to branches of the network while the rows correspond to

nodes.

Let V$=[$v$\_(1)$v$\_(2)$dotsv$\_(6)]^($TT$)$ denote the vector of branch voltages while I$=[$i$\_(1)$i$\_(2)$dotsi$\_(6)]$T that

of branch currents. The vector E$=[[$e$\_(1),$e$\_(2),$e$\_(3),$e$\_(4)]]^($TT$)$ denotes the vector of node

voltages relative to a common ground.

A$=[[1,1,1,0,0,0],[0,-1,0,-1,1,0],[-1,0,0,0,-1,-1],[0,0,-1,1,0,1]]$

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