I am working on a simultaneous linear equation problem using LU decomposition.
$5x1 + 6x2 + 2.3x3 + 6x4 = 4$
$9x1 + 2x2 + 3.5x3 + 7x4 = 5$
$3.5x1 + 6x2 + 2x3 + 3x4 = 6.7$
$1.5x1 + 2x2 + 1.5x3 + 6x4 = 7.8$
\begin{bmatrix}5&6&2.3&6\\9&2&3.5&7\\3.5&6&2&3\\1.5&2&1.5&6\end{bmatrix}
When calculating the L and U matrix I would need to perform L21 * U11 = 9. However since U11 will be 5 we will not be able to calculate L21.
$L=$ \begin{bmatrix}1&0&0&0\\&1&&\\&&1&\\&&&1\end{bmatrix}
$U=$ \begin{bmatrix}5&6&2.3&6\\&&&\\&&&\\&&&\end{bmatrix}
I have tried asking my tutor to help me understand but he doesn't seem to want to do so. I am very new to this and have done some simple examples involving 2x2 and 3x3 matrices with only integer values. Would appreciate any insight on where I might be going wrong or how I would solve this simultaneous linear equation.