Let \(A=\begin{bmatrix}1 & 2\\-1 & 1\end{bmatrix}\) and \(C=\begin{bmatrix}-1 & 1\\2 & 1\end{bmatrix}\). Find elementary matrices \(E_1\) and \(E_2\) such that \(C=E_2E_1A\).
\[E_1=\begin{bmatrix}\answer {1} & \answer {-1}\\\answer {0} & \answer {1}\end{bmatrix};\quad E_2=\begin{bmatrix}\answer {0} & \answer {1}\\\answer {1} & \answer {0}\end{bmatrix}\]

Source

[Nicholson] W. Keith Nicholson, Linear Algebra with Applications, Lyryx 2021, Open Edition, Problem 2.5.3 (a).