LU-Decomposition

Sep 2011
105
1
How do I solve (i)?
 

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Jun 2019
493
260
USA
Only A3 has a "proper" LU decomposition (without pivoting). Hopefully this much you had no problem with.

As far as finding the decomposition, there are a number of algorithms you can find online. However, for 3x3 it is easy enough to solve on your own.

\(\displaystyle A=\begin{bmatrix} 1 & 0 & 0 \\ l_{2,1} & 1 & 0 \\ l_{3,1} & l_{3,2} & 1\end{bmatrix} \begin{bmatrix} u_{1,1} & u_{1,2} & u_{1,3} \\ 0 & u_{2,2} & u_{2,3} \\ 0 & 0 & u_{3,3} \end{bmatrix}\)
Nine equations, nine unknowns.
 
Sep 2011
105
1
Thank you. I got it.

How would I approach part (ii)?