## Solving Simultaneous Equations Using LU Decomposition

Given a system of linear equations in the formwe can use the LU factorisation ofto solve the linear systemin a two-step triangular process.

Letso thatThe solution is obtained by solving recursively the two systems

and

Example: Use LU decomposition to solve

x-2y+3z=4

2x-5y+12z=6

2y-10z=3

we can write the matrix form of the system

The matrix decomposes:

We solve

|From which

Now solve

We have

The original system of equations is