- #1
Dafe
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Homework Statement
With conductances [tex]c_{1}=1, c_{2}=c_{3}=2[/tex], multiply matrices to find
[tex] A^TCAx = f [/tex].
For [tex] f = (1,0,-1) [/tex] find a solution to [tex] A^TCAx = f [/tex].
Write the potentials [tex] x [/tex] and currents [tex] y = -CAx [/tex] on the triangle graph, when the current source [tex] f [/tex] goes into node 1 and out from node 3.
Homework Equations
The Attempt at a Solution
[tex]
A^TCA =
\left[ \begin{array}{ccc} 3 & -1 & -2 \\ -1 & 3 & -2 \\ -2 & -2 & 4 \\ \end{array} \right]
[/tex]
After elimination I get:
[tex]
A^TCA =
\left[ \begin{array}{cccc} 3 & -1 & -2 & 1 \\ 0 & 8 & -8 & 1 \\ 0 & 0 & 0 & 0 \\ \end{array} \right]
[/tex]
Which to me means that the loop is broken, and that [tex] x_{3} [/tex] is a free variable.
The book chooses [tex] x_{3}=7/8 [/tex]. Is there a good reason for that value?
Maybe I am missing some important point here?
Thanks.