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Linear Algebra and the C Language/a04g
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Network analysis
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We can write:
Input = Output
A = x1 = 20 + x2
B = x2 + x3 + x5 = 60
C = x4 = 20 + x3
D = 100 = x1 + x4 + x5
We write: x2 = 10 and x5 = 30
A = x1 = 20 + 10
B = 10 + x3 + 30 = 60
C = x4 = 20 + x3
D = 100 = x1 + x4 + 30
Let's rectify the system
x1 = 20 + 10
x3 = 60 - 10 -30
x4 - x3 = 20
-x1 - x4 = -100 + 30
Now:
x1 +0 +0 +0 20 + 10 // A
+0 x3 +0 +0 60 - 10 -30 // B
+0 -x3 x4 +0 +20 // C
-x1 +0 -x4 +0 -100 + 30 // D
The code in C language:
double ab[RA*(CA+Cb)]={
// x1 x3 x4
+1, +0, +0, +0, +20+10, // A
+0, +1, +0, +0, +60 -10 -30, // B
+0, -1, +1, +0, +20, // C
-1, +0, -1, +0, -100+30, // D
};
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The solution is given by solving the system:
x1 x3 x4
+1 +0 +0 +0 +30
+0 +1 +0 +0 +20
+0 +0 +1 +0 +40
+0 +0 +0 +0 +0
x1 = +30; x3 = +20; x4 = +40;
With x2 = +10; x5 = +30;