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# Solving linear systems using LU factorisation

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Solve the system Ax = b by doing LU factorization.

** Please see the attached file for the complete problem description **

##### Solution Summary

This solution explains LU factorization and how it can be used to solve a system of linear equations, using a step by step breakdown of a real example of a system of four equations with four variables (4x4).

##### Solution Preview

** Please see the attached file for the complete solution explanation **

To solve a system Ax = b doing LU factorization we let A = LU and then substitute into the original equation i.e. Ax = b therefore getting LUx = b. We then solve the system Ux = y Ly = b and Ux = y where we first solve Ly = b to find y and then substitute y into Ux = y to find x

So for:

We need to find L and U for which A=LU
We need to perform row operations on matrix A where (please see the attached file) to form the Upper triangular matrix while at the same time using the opposite of the multiplier we also form the Lower ...

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