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    Matrix Factorization for solving linear equations

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

    © BrainMass Inc. brainmass.com October 10, 2019, 2:41 am ad1c9bdddf
    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