Chapter 6.5, Problem 17E

To determine

To find:

The elementary matrices $E_1$, $E_2$, and $E_3$ and the value of the product $Q=E_1{E}_2{E}_3$ and verify that $AQ=L$ and $\det \left(Q\right)=\det \left(Q^T\right)$.

$A=\left[\begin{array}{ccc}0& 1& 3\\ 1& 2& 4\\ 2& 2& 1\end{array}\right]$