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Solving Linear system of equations Mathematics.pdf.pptx
1. Masters in Electrical & Microsystems
Engineering
Advanced Engineering Mathematics
Linear Systems Electric AC Circuit
Presented by:
Nima Aminfar (3362365)
Omer Rahama (3359754)
2.
3. By applying Kirchhoff `s current law for points 1,2,3∶
𝐼𝑅4
𝐼𝑅1 𝐼𝑅2 𝐼𝑅3
𝐼𝑅5
𝐼𝑅6
𝐼𝐶1 𝐼𝐶2
𝐼𝑅1 − 𝐼𝐶1−𝐼𝑅4= 0
𝐼𝑅2 + 𝐼𝐶1 −𝐼𝑅5 −𝐼𝐶2 = 0
𝐼𝑅3 + 𝐼𝐶2−𝐼𝑅6= 0
8. So the matrix will be:
=
*
(𝟏. 𝟓 + 𝒊)
X1 = 1.69369 − 0.162162 i
-𝒊
𝑿𝟐
0
𝑿𝟑
−𝒊 (𝟏. 𝟓 + 𝟏. 𝟓 𝒊) −𝟎. 𝟓 𝒊
0 -0.𝟓 𝒊 (𝟏. 𝟓 + 𝟎. 𝟓 𝒊)
3
1.5
3
𝑿𝟏
X2= 1.45045 + (0.297297) i X3= 1.85586 − (0.135135) i
9. Gaussian elimination Method:
• Gauss Elimination Method is a procedure for solving systems of linear equation. It is also known as Row
Reduction Technique.
• In this method, the problem of systems of linear equation having n unknown variables, matrix having rows
n and columns n+1 is formed. This matrix is also known as Augmented Matrix.
• After forming n x n+1 matrix, matrix is transformed to upper triangular matrix by row operations. Finally
result is obtained by Back Substitution.
• In this project, we are dealing with 3 unknown variables . So the Augmented Matrix would be 3*4.
10. Definition Of Complex
Numbers
Enter The Value Of
The Matrix
Check 1st
diagonal is
zero
Gauss Elimination Can
Not Performed
Check The
Determina
nt is Zero
Gauss Elimination Can
Not Performed
Start
End
End
Proceed To Enter
Vector b
Print The Values Of
V1, V2, V3 and Phases
in degree
Print The Values Of
𝑋1, 𝑋2, 𝑋3
End
Flowchart Of The Program:
Yes
Yes
No
No
Start The Gauss
Elimination Process