Answer
$L=\left[\begin{array}{cc}1 & 0 \\ -3 / 2 & 1\end{array}\right], U=\left[\begin{array}{cc}2 & 5 \\ 0 & 3.5\end{array}\right]$
Work Step by Step
First reduce matrix $A$ to row echelon form which represents matrix $U$.
$\left[\begin{array}{cc}\frac{2}{-3} & -4\end{array}\right],$ multiply first row with $3 / 2$ and add to second
$\sim\left[\begin{array}{cc}2 & 5 \\ 0 & 3.5\end{array}\right]=U$
Both columns of matrix $U$ are pivot columns. Put those columns (underlined elements) into matrix
$\left[\begin{array}{cc}2 & 0 \\ -3 & 3.5\end{array}\right]$
Now to get matrix $L$ divide each column with leading element. First column with 2 and second with 3.5 .
$L=\left[\begin{array}{cc}1 & 0 \\ -3 / 2 & 1\end{array}\right]$
