$$A=\begin{pmatrix} 1 & 4 & 2\\ 0 & 2 & 1\\ 3 & 5 & 3 \end{pmatrix}, \quad B=\begin{pmatrix} 1\\ 2\\ 3 \end{pmatrix}.$$ $A$ is $3\times3$ matrix and $B$ is $3\times1$ matrix. Using these two matrices, I have to answer the following $3$ questions.
- Find $L$ and $U$ that satisfy $A=LU$
- Find $Y$ that satisfies $LY=B$.
- 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.
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 $U.$