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Matrix Factorization for solving linear equations

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Require examples and procedure of:
- Solving Linear Equation - Ax = b
- Matrix Factorization - A = LU

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Solution Summary

Matrix Factorization is clearly demonstrated.

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Gauss Elimination.
We would like to solve the system

Where is a marrix, is the variables vectors and is the constant solution vector.
If we can transform the matrix A into an upper triangular matrix U such that:

By using linear row operations, then the system will be written as:

Where is the result of applying the same operation on the solution vector b.
Then we can use backwards ...

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