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Linear Algebra and the C Language/a04k
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Network analysis
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We can write:
Input = Output
A = x1 + x2 = 50
B = 40 = x2 + x3
C = x3 + x4 = 20
D = 30 = x1 + x4
We write x4 = 10
A = x1 + x2 = 50
B = 40 = x2 + x3
C = x3 + 10 = 20
D = 30 = x1 + 10
Let's rectify the system
x1 + x2 = 50
-x2 - x3 = -40
x3 = 20 -10
-x1 = -30 + 10
Now:
x1 x2 x3
+x1 +x2 +0 +0 +50 // A
+0 -x2 -x3 +0 -40 // B
+0 +0 +x3 +0 +20 -10 // C
-x1 +0 +0 +0 -30 +10 // D
The code in C language:
double ab[RA*(CA+Cb)]={
// x1 x2 x3
+1, +1, +0, +0, +50, // A
+0, -1, -1, +0, -40, // B
+0, +0, +1, +0, +20 -10, // C
-1, +0, +0, +0, -30 +10 // D
};
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The solution is given by solving the system:
x1 x2 x3
+1 +0 +0 +0 +20
-0 +1 +0 -0 +30
+0 +0 +1 +0 +10
+0 +0 +0 +0 +0
x1 = 20; x2 = 30; x3 = 10;
With x4 = 10