Linear Equation System Study on Electrical Circuits Using Matlab

In everyday life, especially in the electrical circuit, there are many usage of matrix. One use of a matrix is found in the system of linear equations. In the field of electrical circuits there are also problems involving systems of linear equations in matrix form. To solve the system of linear equations in matrix form, in addition to using elementary row operations, also used matlab.


INTRODUCTION
In the field of scientific engineering, known to many branches of science such as civil engineering sciences, electrical engineering and information engineering sciences.In the science of electrical engineering, there are various problems such as science of electric field phenomena, telecommunications engineering science and electrical circuitry.In the science of electrical circuits, also known kirchoff laws.There are two kirchoff laws: first kirchoff law and second kirchoff law.Using both kirchoff laws, a linear equation system can be established.
If in an electrical circuit, there is one loop, then only one linear equation system will be formed.Where there are more than one loop, more than one system of linear equations can be formed, according to the number of loops available.If there are many linear equations, it would be easy to construct a system of linear equations.
To solve the system of linear equations, it can be used several ways such as substitution method, elimination method.Both of these methods are suitable for solving systems of linear equations that have only two variables.If the system of linear equations has more than two variables, then the solution of this system of linear equations, using elementary row operation methods and also using matlab.
MATLAB is short for MATrix LABoratory because every data in MATLAB uses basic matrix.MATLAB is a high, closed, and case sensitive programming language in numerical computing environments developed by MathWorks.One of its most popular advantages is the ability to create graphics with the best customization support.
MATLAB has many tools that can help various disciplines.This is one of the causes of industry using MATLAB.In addition MATLAB has many libraries that are helpful for solving mathematical problems such as simulating functions, mathematical modeling and GUI design. MATLAB

TYPES OF MATRICES
There are various types of matrices that are adjusted to the order and position of the elements.The types of matrices are: 1. Square Matrix The square matrix is the matrix with the number of rows and the same number of columns nx n.An example of a square matrix is a 2 x 2 matrix.2. Diagonal matrix Is a square matrix in which elements other than the diagonal element are 0. The diagonal element is the element aij where i = j.

Identity Matrix
It is a diagonal matrix whose all diagonal elements are 1.

Unit Matrix
Is a matrix whose elements contain only one or zero.

Triangle Matrix
There are two divisions.Namely the upper triangular matrix is the square matrix that all elements below the diagonal element are zero.
In contrast the lower triangular matrix is a square matrix that all elements above the diagonal element are zero.

Symmetry Matrix
Is a square matrix where for each element in the index row i column j, it has the same value as the element in the row index of column i. (aij = aji).

TERMS ON MATRIX 1. Transpose Matrix
The transpose matrix is denoted by At.Trasposing a matrix A can be done by converting the row in the matrix A into the column of the At matrix 2.Determinate Matrices The determinant of the matrix is a scalar function with the square matrix domain.Determinants in the matrix are used in analyzing a matrix such as checking for the absence of an inverse matrix, determining system solutions of linear equations, vector base checks and others.The determinant of a matrix is represented by replacing the square brackets in the matrix into a downward vertical line.

Inverse Matrix
If there is a square matrix A and B and of the same order, and I is the identity matrix.If there is an equation A. B = I, then it can be said that B is the inverse of A, and A is the inverse of B. Invers is denoted by a negative one.In this case A -1 = B, and B -1 = A.

OPERATION ON MATRICES
In the matrix there are also operations.Operations that can be done on the matrix include:

Matrix summation
The sum of the matrix can only be applied to matrices having the same order size.If A = (aij) and B = (bij) are equal-sized matrices, then A + B is a matrix C = (cij) where (cij) = (aij) + (bij) or have the same size and element (cij) = (aij) + (bij).

Matrix Reduction
As with matrix summation, matrix reduction can only be done on matrices of the same size.If the size is different then the result matrix is undefined.

Multiplication of Matrix Scalar
If k is a scalar number and A = (aij) then the matrix kA = (kaij) is a kA matrix obtained by multiplying all elements of matrix A with k.Multiplying a matrix with a scalar can be written in front of or behind the matrix.For example

Multiplication Matrix with Matrix
If A is the matrix of the mx n and B is the n xp pacing matrix, then the matrix A product with B, eg C, is the new matrix of the m x p beam.

The Matrix of Cage Length
If A is a rectangular matrix, then the appointment of matrix A is defined as follows.If A is a rectangular matrix, then the appointment of matrix A is defined as follows.

E. LEGAL MATRIX
If A, B, and C are equivalent matrices to be multiplied, then the matrix multiplication properties are applied: Not commutative, Associative, Distributive and There is an identity matrix I so that AI = IA = A.

KIRCHOFF's FIRST LAW
This law states that the current entering the branching point is as large as the current leaving the point.If i1 and i4 are currents entering the branching point, whereas i2 and i3 are currents coming out of the branching point, i1 + i4 = i2 + i3.This is called Kirchhoff's Law, Kirchhoff's point law, Kirchhoff branching law, or KCL (Kirchhoff's Current Law).The principle of conservation of electric charge says that: At each branching point in the electrical circuit, the sum of the currents entering the point is equal to the amount of current coming out of that point.Or The total number of currents at a point is zero.Whereas the second law of kirchoff states the sum of all voltages around the loop (round) equal to zero.

OPERATION LINE ELEMENTER (OBE)
The elementary row operation (OBE) is an operation performed in order to simplify an augmented matrix.OBE in the process is an arithmetic operation (involving addition and multiplication) imposed on each element in a certain row of a matrix.In the process the elementary row operations include: 1. Line exchange 2. Multiplication of a row with non-zero constants 3. The sum of a row with the other row multiplication with non-zero constants.

II. METHODOLOGY Diagram Block Research
The research block diagram is written as follows:

Case Study
In the above sequence, if R 3 is known to be 4 ohm, R 1 is 4 ohms, and R 2 is 2 ohms, and V is 10 volts.Determine I 1 , I 2 , and I 3 !

Resolution:
In Based on the above calculation results can be concluded the value of the variable I 1 = 5 amperes, I 2 = 10 amperes and I 3 = 2.5 amperes.