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