# Linear Algebra: Matrix [closed]

$$A=\begin{pmatrix} 1 & 4 & 2\\ 0 & 2 & 1\\ 3 & 5 & 3 \end{pmatrix}, \quad B=\begin{pmatrix} 1\\ 2\\ 3 \end{pmatrix}.$$ $A$ is $3\times3$ matrix and $B$ is $3\times1$ matrix. Using these two matrices, I have to answer the following $3$ questions.

1. Find $L$ and $U$ that satisfy $A=LU$
2. Find $Y$ that satisfies $LY=B$.
3. Find $X$ that satisfies $UX=Y$.

I don't even know how to start these questions... Plus, I apologize for not knowing how to write a matrix in this website.

## closed as off-topic by Chris Godsil, José Carlos Santos, hardmath, Servaes, GNUSupporter 8964民主女神 地下教會Apr 19 '18 at 20:29

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• What are the conditions on $L,U,Y$ and $X$ (what dimension, what vector space)? – Bill O'Haran Apr 19 '18 at 12:50
• Can it be that you missed the course on $LU$ decomposition ? – Yves Daoust Apr 19 '18 at 12:57

Find the reduced echelon form of $$A=\begin{pmatrix} 1 & 4 & 2\\ 0 & 2 & 1\\ 3 & 5 & 3 \end{pmatrix}$$
That is your $U$
Now you can find your $L$ easily from $A$ and $U.$