Find the LU decomposition of A=[123254485]A = \begin{bmatrix} 1 & 2 & 3 \\ 2 & 5 & 4 \\ 4 & 8 & 5 \end{bmatrix}A=124258345. Which option is correct?
L=[100210401]L = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 4 & 0 & 1 \end{bmatrix}L=124010001, U=[12301−200−7]U = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & -2 \\ 0 & 0 & -7 \end{bmatrix}U=1002103−2−7
L=[100210411]L = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 4 & 1 & 1 \end{bmatrix}L=124011001, U=[12301−2003]U = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & -2 \\ 0 & 0 & 3 \end{bmatrix}U=1002103−23
L=[1001104−21]L = \begin{bmatrix} 1 & 0 & 0 \\ 1 & 1 & 0 \\ 4 & -2 & 1 \end{bmatrix}L=11401−2001, U=[12303100−7]U = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 3 & 1 \\ 0 & 0 & -7 \end{bmatrix}U=10023031−7
L=[100210401]L = \begin{bmatrix} 1 & 0 & 0 \\ 2 & 1 & 0 \\ 4 & 0 & 1 \end{bmatrix}L=124010001, U=[123012007]U = \begin{bmatrix} 1 & 2 & 3 \\ 0 & 1 & 2 \\ 0 & 0 & 7 \end{bmatrix}U=100210327