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3.2: LU Decomposition
https://math.libretexts.org/Bookshelves/Applied_Mathematics/Numerical_Methods_(Chasnov)/03%3A_System_of_Equations/3.02%3A_LU_Decomposition
We now illustrate the solution of $L U \mathbf{x}=\mathbf{b}$ using our previous example, where \[\mathrm{L}=\left( $\begin{array}{rrr} 1 & 0 & 0 \\ -2 & 1 & 0 \\ -1 & 1 & 1 \end{array}$ \right), \quad ...We now illustrate the solution of $L U \mathbf{x}=\mathbf{b}$ using our previous example, where $\mathrm{L}=\left(\begin{array}{rrr} 1 & 0 & 0 \\ -2 & 1 & 0 \\ -1 & 1 & 1 \end{array}\right), \quad \mathrm{U}=\left(\begin{array}{rrr} -3 & 2 & -1 \\ 0 & -2 & 5 \\ 0 & 0 & -2 \end{array}\right), \quad \mathbf{b}=\left(\begin{array}{l} -1 \\ -7 \\ -6 \end{array}\right) \nonumber$ With $\mathbf{y}=\mathbf{U x}$ , we first solve $\mathbf{L} \mathbf{y}=\mathbf{b}$ , that is \[\left(\begin{array}…

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