I have the following equation, where I need to find what the matrix $X$ is equal to:
\begin{bmatrix}1&1\\1&1\end{bmatrix} \begin{bmatrix}2&3\\2&3\end{bmatrix}
Let's say the first matrix is $A$, and the second one is $B$, then I need to find $AX=B$. $%(I'm sorry if I'm not writing this out properly, I don't know the all the codes I need to use. If someone could edit it I would be grateful.)$
Now normally the way I would solve this is to combine matrices $A$ and $B$ in such a way:
\begin{bmatrix}1&1&2&3\\1&1&2&3\end{bmatrix}
And try to change the product matrix in such a way that I would get the identity matrix in place of $A$ and at the same time get the matrix $X$ in place of $B$. Clearly that doesn't work in my example, because I can't get the identity matrix out of $A$. So then how could I solve this problem? Any suggestions? Help would be greatly appreciated.
Note that
$$A*X=B$$
correspond to the following systems
$$\begin{bmatrix}1&1\\1&1\end{bmatrix}x_1=\begin{bmatrix}2\\2\end{bmatrix}$$
$$\begin{bmatrix}1&1\\1&1\end{bmatrix}x_2=\begin{bmatrix}3\\3\end{bmatrix}$$
with $x_1$ and $x_2$ columns of X.