Guassian Elimination implemented to solve 3,4 degree equations and serve it in web service with random generated equations
go run main.go
Test at : http://localhost:8080/show3 : For 3 degree equations
For 4 degree equations : http://localhost:8080/show4
What is the Gauss Elimination Method?
In mathematics, the Gaussian elimination method is known as the row reduction algorithm for solving linear equations systems. It consists of a sequence of operations performed on the corresponding matrix of coefficients. We can also use this method to estimate either of the following:
The rank of the given matrix The determinant of a square matrix The inverse of an invertible matrix To perform row reduction on a matrix, we have to complete a sequence of elementary row operations to transform the matrix till we get 0s (i.e., zeros) on the lower left-hand corner of the matrix as much as possible. That means the obtained matrix should be an upper triangular matrix. There are three types of elementary row operations; they are:
Swapping two rows and this can be expressed using the notation ↔, for example, R2 ↔ R3 Multiplying a row by a nonzero number, for example, R1 → kR2 where k is some nonzero number Adding a multiple of one row to another row, for example, R2 → R2 + 3R1 Learn more about the elementary operations of a matrix here.
The obtained matrix will be in row echelon form. The matrix is said to be in reduced row-echelon form when all of the leading coefficients equal 1, and every column containing a leading coefficient has zeros elsewhere.
[ Reference for the above method explanations here is : https://byjus.com/maths/gauss-elimination-method/#:~:text=In%20mathematics%2C%20the%20Gaussian%20elimination,the%20corresponding%20matrix%20of%20coefficients. ]
There are two major functions :
Forward elimination : To convert to row-echeleon method.
Backward Substituiton : To convert to reduced row echeleon form. [ Where the actual solution for finite solution based consistent equations are obtained ]