Consider solving the following system of simultaneous equations using LU decomposition. $$\begin{aligned} x_1 + x_2 - 2x_3 &= 4 x_1 + 3x_2 - x_3 &= 7 \\ 2x_1 + x_2 - 5x_3 &= 7 \end{aligned}$$ where $L$ and $U$ are denoted as $$L = \begin{pmatrix} L_{11} & 0 & 0 \\ L_{21} & L_{22} & 0 \\ L_{31} & L_{32} & L_{33} \end{pmatrix}, \quad U = \begin{pmatrix} U_{11} & U_{12} & U_{13} \\ 0 & U_{22} & U_{23} \\ 0 & 0 & U_{33} \end{pmatrix}$$ Which one of the following is the correct combination of values for $L_{32}$, $U_{33}$, and $x_1$?

Consider solving the following system of simultaneous equations using LU decomposition. aligned x1 + x2 - 2x3 &= 4 x1 + 3x2 - x3 &= 7 \\ 2x1 + x2 - 5x3 &= 7 aligned where L and U are denoted as L = pmatrix L11 & 0 & 0 \\ L21 & L22 & 0 \\ L31 & L32 & L33 pmatrix, U = pmatrix U11 & U12 & U13 \\ 0 & U22 & U23 \\ 0 & 0 & U33 pmatrix Which one of the following is the correct combination of values for L32, U33, and x1?

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