# Matrix Factorization for solving linear equations

Require examples and procedure of:

- Solving Linear Equation - Ax = b

- Matrix Factorization - A = LU

https://brainmass.com/math/matrices/matrix-factorization-solving-linear-equations-389125

#### Solution Preview

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 ...

#### Solution Summary

Matrix Factorization is clearly demonstrated.

$2.19