Give the elementary matrix that converts

Question

I am having trouble figuring out the exact elementary row operation required for transforming \begin{bmatrix}1&-2&-2\\-3&-2&3\\-2&4&-1\end{bmatrix} to \begin{bmatrix}-11&-10&-10\\-3&-2&3\\-2&4&-1\end{bmatrix}

I understand how these work, but for this problem I don't know how to go about solving it. Cheers

Answer 1

We have the following equation for a matrix $X$.

$$\begin{bmatrix}1&-2&-2\\-3&-2&3\\-2&4&-1\end{bmatrix}X=\begin{bmatrix}-11&-10&-10\\-3&-2&3\\-2&4&-1\end{bmatrix}$$

Multiplying both side from the left by the inverse of the left most matrix we get

$$X=\begin{bmatrix}1&-2&-2\\-3&-2&3\\-2&4&-1\end{bmatrix}^{-1}\begin{bmatrix}-11&-10&-10\\-3&-2&3\\-2&4&-1\end{bmatrix}.$$

Just proceed from here. (Wolfram Alpha will kindly help.)