Write a program that implements Gaussian elimination method with pivot condensation for solving n linear equations in n variables, that calls procedures (i) lower-triangularisation and (ii) back substitutions (codes of procedures are also to be written). Use the program for solving the following system of linear equations: 5x - 7y + 8z = 11 4x - 9y + 3z = 2 9x +2y + 5z = 25
Answers
Answer:In engineering and science, the solution of linear simultaneous equations is very important. Different analysis such as electronic circuits comprising invariant elements, a network under steady and sinusoidal condition, output of a chemical plant and finding the cost of chemical reactions in such plants require the solution of linear simultaneous equations.
In Gauss-Elimination method, these equations are solved by eliminating the unknowns successively. The C program for Gauss elimination method reduces the system to an upper triangular matrix from which the unknowns are derived by the use of backward substitution method.
Pivoting, partial or complete, can be done in Gauss Elimination method. So, this method is somewhat superior to the Gauss Jordan method. This approach, combined with the back substitution, is quite general. It is popularly used and can be well adopted to write a program for Gauss Elimination Method in C.
Step-by-step explanation:
Answer:
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Step-by-step explanation:
The article focuses on using an algorithm for solving a system of linear equations. We will deal with the matrix of coefficients. Gaussian Elimination does not work on singular matrices (they lead to division by zero).
Input: For N unknowns, input is an augmented
matrix of size N x (N+1). One extra
column is for Right Hand Side (RHS)
mat[N][N+1] = {{3.0, 2.0,-4.0, 3.0},
{2.0, 3.0, 3.0, 15.0},
{5.0, -3, 1.0, 14.0}