(5) Consider the application of Ohm's law and Kirchhoff's law to a given electrical net- work. The potential applied between two of the nodes in the network is V volts. We wish to find the potentials at several nodes within the network. Denoting these potentials by U1, U2, U6, we obtain the following set of equations for the v; values: 11v1 - 5v2v6 = 5V, -20v₁ + 41v2 - 15v3 - 6v5 = 0, -3v2+7v3 - 4v4 = 0, - -V3 +2v4v5 = 0, -3v2-10v4 + 28v5 - 1506 (a) Write this linear system in matrix-vector form. = - - 0, 2v1 15v5 + 47v6 = 0. (b) Set V50 and use the software for solving linear systems that was introduced in the recitation to solve this system.

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter11: Nonlinear Programming
Section11.10: Quadratic Programming
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(5) Consider the application of Ohm's law and Kirchhoff's law to a given electrical net-
work. The potential applied between two of the nodes in the network is V volts. We wish
to find the potentials at several nodes within the network. Denoting these potentials by
U1, U2, U6, we obtain the following set of equations for the v; values:
11v1 - 5v2v6 = 5V, -20v₁ + 41v2 - 15v3 - 6v5 = 0, -3v2+7v3 - 4v4 = 0,
-
-V3 +2v4v5 = 0, -3v2-10v4 + 28v5 - 1506
(a) Write this linear system in matrix-vector form.
=
-
-
0, 2v1 15v5 + 47v6
= 0.
(b) Set V50 and use the software for solving linear systems that was introduced in the
recitation to solve this system.
Transcribed Image Text:(5) Consider the application of Ohm's law and Kirchhoff's law to a given electrical net- work. The potential applied between two of the nodes in the network is V volts. We wish to find the potentials at several nodes within the network. Denoting these potentials by U1, U2, U6, we obtain the following set of equations for the v; values: 11v1 - 5v2v6 = 5V, -20v₁ + 41v2 - 15v3 - 6v5 = 0, -3v2+7v3 - 4v4 = 0, - -V3 +2v4v5 = 0, -3v2-10v4 + 28v5 - 1506 (a) Write this linear system in matrix-vector form. = - - 0, 2v1 15v5 + 47v6 = 0. (b) Set V50 and use the software for solving linear systems that was introduced in the recitation to solve this system.
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