Electrical Engineering (EE) Exam > Electrical Engineering (EE) Questions > If [A] Matrix is Incidence matrix then which ...
Start Learning for Free
If [A] Matrix is Incidence matrix then which one of the following is true?
- a)|A| = 0 (For closed loop)
- b)Adj [A] / |A| = 0 (For closed loop)
- c)[A] = 1 (For closed loop)
- d)|A| = 1 (For closed loop)
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
If [A] Matrix is Incidence matrix then which one of the following is t...
Incidence matrix:
- It is the matrix that gives a relation between the branches and nodes.
- The rows of the incidence matrix [A] represent the number of nodes and the column of the matrix represents the number of branches in the given graph.
- If there are ‘n’ number of rows in a given incidence matrix[A], that means in a graph there are ‘n’ number of nodes.
- Similarly, if there are ‘b’ numbers of columns in that given incidence matrix[A], that means in that graph there are ‘b’ number of branches.
- We can construct the incidence matrix for the directed graph. We can draw a graph with the help of the incidence matrix.
- The algebraic sum of elements of all the columns is zero.
- The rank of the incidence matrix is (n–1).
- The determinant of the incidence matrix of a closed loop is zero.
Hence, an Only statement I is correct.
Free Test
FREE
| Start Free Test |
Community Answer
If [A] Matrix is Incidence matrix then which one of the following is t...
Understanding the Incidence Matrix
An incidence matrix is a mathematical representation used in graph theory, particularly in electrical engineering for circuit analysis. Each row represents a node, and each column represents a branch of the network.
Closed Loop in Circuit Theory
In circuit theory, a closed loop refers to a continuous path in which a circuit returns to its original point. This is essential for the analysis of circuits, especially when applying Kirchhoff's laws.
Determinant of the Incidence Matrix
- The determinant of the incidence matrix, denoted as |A|, provides information about the properties of the graph.
- For a closed loop, the determinant of the incidence matrix is always equal to zero (|A| = 0).
Why |A| = 0 for Closed Loops?
- A closed loop indicates that there is a redundancy in the paths, meaning that the matrix does not have full rank.
- When a graph has a closed loop, there are linearly dependent rows in the incidence matrix, leading to a determinant of zero.
Conclusion
Thus, when evaluating the properties of an incidence matrix for a network with a closed loop, the correct assertion is that the determinant of the incidence matrix is zero.
Overall, the assertion that |A| = 0 for a closed loop is a fundamental concept in understanding the relationship between graphs and their matrix representations in electrical engineering.
An incidence matrix is a mathematical representation used in graph theory, particularly in electrical engineering for circuit analysis. Each row represents a node, and each column represents a branch of the network.
Closed Loop in Circuit Theory
In circuit theory, a closed loop refers to a continuous path in which a circuit returns to its original point. This is essential for the analysis of circuits, especially when applying Kirchhoff's laws.
Determinant of the Incidence Matrix
- The determinant of the incidence matrix, denoted as |A|, provides information about the properties of the graph.
- For a closed loop, the determinant of the incidence matrix is always equal to zero (|A| = 0).
Why |A| = 0 for Closed Loops?
- A closed loop indicates that there is a redundancy in the paths, meaning that the matrix does not have full rank.
- When a graph has a closed loop, there are linearly dependent rows in the incidence matrix, leading to a determinant of zero.
Conclusion
Thus, when evaluating the properties of an incidence matrix for a network with a closed loop, the correct assertion is that the determinant of the incidence matrix is zero.
Overall, the assertion that |A| = 0 for a closed loop is a fundamental concept in understanding the relationship between graphs and their matrix representations in electrical engineering.
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Top Courses for Electrical Engineering (EE)View all
Question Description
If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. 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 If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. 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 If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer?.
If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. 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 If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. 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 If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer?.
Solutions for If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for Electrical Engineering (EE).
Download more important topics, notes, lectures and mock test series for Electrical Engineering (EE) Exam by signing up for free.
Here you can find the meaning of If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer?, a detailed solution for If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice If [A] Matrix is Incidence matrix then which one of the following is true?a)|A| = 0 (For closed loop)b)Adj [A] / |A| = 0 (For closed loop)c)[A] = 1 (For closed loop)d)|A| = 1 (For closed loop)Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice Electrical Engineering (EE) tests.
|
|
Explore Courses for Electrical Engineering (EE) exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup