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To find the inverse of a matrix using LU decomposition with $u_{11} = u_{22} = u_{33} = 1$, we first decompose the matrix $A$ into a product of a lower triangular matrix $L$ and an upper triangular matrix $U$. Here, $U$ has ones on its diagonal. Assume $A$ is a $3 \times 3$ matrix ____ _______ ________ ___ _________ _______ ________ ____ __________ ______.
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