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I've been given the matrix $B$ = $\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -1 \\ 2 & 3 & 1 \end{bmatrix}$ and I would like to find the $LU$ decomposition of $B$. I use row operations to obtain the matrix

$U$ =$\begin{bmatrix} 1 & 0 & 1 \\ 0 & 1 & -1 \\ 0 & 0 & 4 \end{bmatrix}$.

I apply these same operations to the matrix

$Z$ =$\begin{bmatrix} 1 & 0 & 0 \\ & 1 & 0 \\ & & 1 \end{bmatrix}$ to get the matrix $L$ =$\begin{bmatrix} 1 & 0 & 0 \\ 0& 1 & 0 \\ -2&-3 & 1 \end{bmatrix}$.

I'd like to know if my $L$ and $U$ in this given decomposition problem are correct?

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  • $\begingroup$ $LU$ should equal $B$ which it doesn’t, so it’s wrong. $\endgroup$ – take008 Mar 23 '18 at 6:31
  • $\begingroup$ That's true. Although, a lot of time would have been saved had someone pointed out that one must apply reverse row operations on $Z$ in order to get the correct matrix $L$. $\endgroup$ – K.M Mar 23 '18 at 6:50
  • $\begingroup$ Like ten seconds. Once you actually multiplied them out, you would have seen that it gave you negative your bottom row. $\endgroup$ – take008 Mar 23 '18 at 7:02
  • $\begingroup$ Not my point, but let's move on. $\endgroup$ – K.M Mar 23 '18 at 7:11
  • $\begingroup$ You should have a $1/2$ in the third row. $\endgroup$ – badatmath Mar 23 '18 at 7:20

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