Q35

Consider solving the following system of simultaneous equations using $\text{LU}$ decomposition.

$$x_{1} + x_{2} – 2x_{3} = 4$$ $$x_{1} + 3x_{2} – x_{3} = 7$$ $$2x_{1} + x_{2} – 5x_{3} = 7$$

where $\textit{L}$ and $\textit{U}$ are denoted as $L = \begin{pmatrix}L_{11} & 0 & 0 \\ L_{21} & L_{22} & 0 \\ L_{31} & L_{32} & L_{33} \end{pmatrix} , U = \begin{pmatrix}U_{11} & U_{12} & U_{13} \\ 0 & U_{22} & U_{23} \\ 0 & 0 & U_{33} \end{pmatrix}$ Which one of the following is the correct combination of values for $\textit{L}_{32}, \textit{U}_{33},$ and $x_{1}?$