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Following is not the property of a complete incidence matrix:
  • a)
    Algebraic sum of the column entries of an incidence matrix is zero
  • b)
    The rank of a complete incidence matrix of a connected graph is (n - 1), where n is total number of nodes
  • c)
    Order of a complete incidence matrix will be (n × b), where b is total number of branches and n is total number of nodes
  • d)
    Determinant of the incidence matrix of a closed loop is not zero.
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Following is not the property of a complete incidence matrix:a)Algebra...
Incidence matrix:
  • It is the matrix which gives relation between branches and nodes.
  • The rows of matrix represent the number of nodes and the columns of matrix represents the numbers of branches.
  • We can construct the incidence matrix for the directed graph. We can draw a graph with the help of incidence matrix.
  • The algebraic sum of elements of all the columns is zero.
  • The rank of incidence matrix is (n–1).
  • The order of  incidence matrix will be (n × b).
  • The determinant of the incidence matrix of a closed loop is zero.
The elements of incidence matrix are given by [A] = [aij]n × b
Where aij = 1, if jth branch is incident at ith node and oriented away.
aij = -1, if jth branch is incident at ith node and oriented towards.
aij = 0, if jth branch is not incident at ith node
b is total number of branches
n is total number of nodes
Reduced incidence matrix:
  • If one of the nodes in the given graph is considered as reference node, then that row can be neglected by writing incidence matrix is called as reduced incidence matrix.
  • The order of reduced incidence matrix is (n – 1) × b.
  • The Algebraic sum of some of the columns is not zero.
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Following is not the property of a complete incidence matrix:a)Algebraic sum of the column entries of an incidence matrix is zerob)The rank of a complete incidence matrix of a connected graph is (n - 1), where n is total number of nodesc)Order of a complete incidence matrix will be (n × b), where b is total number of branches and n is total number of nodesd)Determinant of the incidence matrix of a closed loop is not zero.Correct answer is option 'D'. Can you explain this answer? for Electrical Engineering (EE) 2025 is part of Electrical Engineering (EE) preparation. The Question and answers have been prepared according to the Electrical Engineering (EE) exam syllabus. Information about Following is not the property of a complete incidence matrix:a)Algebraic sum of the column entries of an incidence matrix is zerob)The rank of a complete incidence matrix of a connected graph is (n - 1), where n is total number of nodesc)Order of a complete incidence matrix will be (n × b), where b is total number of branches and n is total number of nodesd)Determinant of the incidence matrix of a closed loop is not zero.Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for Electrical Engineering (EE) 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Following is not the property of a complete incidence matrix:a)Algebraic sum of the column entries of an incidence matrix is zerob)The rank of a complete incidence matrix of a connected graph is (n - 1), where n is total number of nodesc)Order of a complete incidence matrix will be (n × b), where b is total number of branches and n is total number of nodesd)Determinant of the incidence matrix of a closed loop is not zero.Correct answer is option 'D'. Can you explain this answer?.
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