5. Find $A = LU$, where $L$ is a lower unit triangular matrix and $U$ is an upper triangular matrix, by (1) solving linear equations sequentially, (2) row operations. (3) Solve $Ax = b$ by two-step substitutions. $\begin{pmatrix} 2 & 0 & -2 \ -4 & 3 & 6 \ 2 & -9 & -9 \end{pmatrix}$, $b = \begin{pmatrix} 0 \ -1 \ 2 \end{pmatrix}$
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The LU decomposition is a factorization of a matrix into a lower triangular matrix L and an upper triangular matrix U. Let A = LU, where L is a lower unit triangular matrix and U is an upper triangular matrix. Suppose we have a system of linear equations Ax = b. Show more…
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