Analysis of an Electrical Network

EXAMPLE: 

• Applying Kirchhoff's Law to have the Linear equations in the variables.
• Below the linear equations is the Augmented and Gauss-Jordan elimination.

Kirchoff's Law

Kirchhoff's Law is an analysis of such a system uses two properties of electrical networks or two equalities that deal with the current and potential difference in the lumped element model of electrical circuits.

1. All current flowing into a junction must flow out of it.

2. The sum of the products IR ( I is current and  R is resistance ) around a closed path is equal to the total voltage in the path.

EXAMPLE:

a.

b.

c.

d.

Solution: 

Network Analysis

Network Analysis - composed of branches and junctions are used as models in many diverse fields such as economics, traffic analysis, and electrical engineering.

EXAMPLE: 

Polynomial Curve Fitting

EXAMPLES :

 



 

1.

 

2.



Homogeneous System

A homogeneous system of linear algebraic equations is one in which all the numbers on the right hand side are equal to 0:

a11x1 + : : : + a1nxn = 0

...

am1x1 + : : : + amnxn = 0

EXAMPLE:

 

(0,0,0) - trivial or obvious solution

Gauss- Jordan Elimination

• Gauss- Jordan Elimination

                    - A method of solving a linear system of equations. This is done by transforming the system's augmented matrix into reduced row-echelon form by means of row operations.

1. Write the Augmented Matrix
2. Target: Reduced Row Echelon Form
3. Rewrite in linear systems

Gaussian Elemination with Back Substitution

1. Write the augmented matrix
2. Use Elementary Row Operations to obtain Row Echelon form of the matrix
3. Rewrite in linear system
4.Back Substitution