Q4. Prove that the LU factorization is unique by considering the possibility that LU = LŨ, for some L, L lower triangular matrices, U,Ũ upper triangular matrices, such that L+L or U # U. (Hint: you will need HW 2 Q3, and discussion week 2 Q3.) Note: For the LU decomposition, we always choose L such that it has only 1s on its diagonal. You should assume this property for L and L.

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