Word Count : 270

---

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 with elements $a_{ij}$. We write $A = LU$, where $$ L = \begin{bmatrix} _______ ___ ________ _______ _________ ________ __________ ______ ___ ____ _____.
____ _______ _____ ______ _____ ____ __________ ____.
__________ _________ ___ _______ ____ __________ ______ ___ ____ _______.
_______ ____ _______ _________ _______.
___ _________ _____ ______ ___ __________.
________ ____ _______ _________ _______ __________.
________ ______ _______ ______ __________ ______ ____ ________.
_______ ___ __________ _____ _________ __________ ____ ______ ___ ______ ____ ________.
______ _______ ___ _________ _______ ____ ______ _______ _______ __________ _______ __________.
_____ _________ ___ _____ __________ _______ __________ _____ _________.
______ ____ ___ ______ __________ _______ _______ _____.
_____ ______ _________ _____ _________.
_____ _____ _________ _______ ___ ________ ____.
____ ____ _______ ____ _______ ________ _____ _______ ________ ______.
_____ ____ _______ ____ _________ __________ ______ ______ ______ ______ ______ __________.
______ __________ ___ ____ _______.
____ _________ ___ _______ _______ ______ _____ ___ _____ _________.
_______ ______ _____ _________ __________ _______ ___ ______.
_______ ____ __________ __________ _____ ________ __________ __________ ___ __________ _________ ______.
__________ _______ _________ _____ _____ ________ ______ _________ _______ ___.
________ ________ _______ _____ ___.
_____ ________ ____ ________ _________ _________ _____.
___ _________ ___ ______ _______.
____ ___ __________ ___ ___ _______ ________ ______ _____ ____ _____.
__________.
Get Full Answer on WhatsApp