number and direct the branches. This we do arbitrarily. The network can now be described by a matrix A = [ajk], where (+1 if branch k leaves node O -1 if branch k enters node O O if branch k does not touch node ajk A is called the nodal incidence matrix of the network. Show that for the network in Fig. 155 the matrix A has the given form. 3 Branch Node (1) Node (2) (Reference node) Node (3) 2.
number and direct the branches. This we do arbitrarily. The network can now be described by a matrix A = [ajk], where (+1 if branch k leaves node O -1 if branch k enters node O O if branch k does not touch node ajk A is called the nodal incidence matrix of the network. Show that for the network in Fig. 155 the matrix A has the given form. 3 Branch Node (1) Node (2) (Reference node) Node (3) 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
Show step-by-step solution
![(a) Nodal Incidence Matrix. The network in Fig. 155
consists of six branches (connections) and four nodes
(points where two or more branches come together).
One node is the reference node (grounded node, whose
voltage is zero). We number the other nodes and
number and direct the branches. This we do arbitrarily.
The network can now be described by a matrix
A = [ajx], where
+1 if branch k leaves node
i branch k enters node O
O if branch k does not touch node
ajk
A is called the nodal incidence matrix of the network.
Show that for the network in Fig. 155 the matrix A has
the given form.
1 2 3 4 5
Branch
6.
Node 1
-1
-1
Node 2
1
1
1.
(Reference node)
Node 3 0
0 1 0 -1
-1
Fig. 155. Network and nodal incidence
matrix in Team Project 20(a)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F65ed85fc-2e75-42cf-bafa-fcdf3f52088e%2Ff04078a8-0686-4675-82b7-d59f84aadc80%2Fwfor7e_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Nodal Incidence Matrix. The network in Fig. 155
consists of six branches (connections) and four nodes
(points where two or more branches come together).
One node is the reference node (grounded node, whose
voltage is zero). We number the other nodes and
number and direct the branches. This we do arbitrarily.
The network can now be described by a matrix
A = [ajx], where
+1 if branch k leaves node
i branch k enters node O
O if branch k does not touch node
ajk
A is called the nodal incidence matrix of the network.
Show that for the network in Fig. 155 the matrix A has
the given form.
1 2 3 4 5
Branch
6.
Node 1
-1
-1
Node 2
1
1
1.
(Reference node)
Node 3 0
0 1 0 -1
-1
Fig. 155. Network and nodal incidence
matrix in Team Project 20(a)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, advanced-math and related others by exploring similar questions and additional content below.Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
