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    Solving linear systems using LU factorisation

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    Please help me with this problem:
    Solve the system Ax = b by doing LU factorization.

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

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    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:
    (please see the attached file)

    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 ...

    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).