August 21st, 2019, 10:43 PM  #1 
Senior Member Joined: Sep 2011 Posts: 102 Thanks: 1  LUDecomposition
How do I solve (i)?
Last edited by skipjack; August 22nd, 2019 at 09:26 PM. 
August 22nd, 2019, 05:53 AM  #2 
Senior Member Joined: Jun 2019 From: USA Posts: 213 Thanks: 90 
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. 
August 22nd, 2019, 07:52 PM  #3 
Senior Member Joined: Sep 2011 Posts: 102 Thanks: 1 
Thank you. I got it. How would I approach part (ii)? 

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