Got the following problem where I can't find a way to solve:
Knowing $\begin{pmatrix}5\\ 3\\ 6\end{pmatrix}$ is the unique solution for the system $Ax=\begin{pmatrix}2\\1\\1\end{pmatrix}$, with $A \in \mathbb{R}^{3\times3}$
and $B=\begin{pmatrix} 1 & 2 & 1 & 2 \\ 1 & 0 & 4 & -1 \\ 1 & 3 & -3 & 6 \end{pmatrix}$
Find all solutions for $ABx=\begin{pmatrix}2\\1\\1\end{pmatrix}$
What I've tried:
- The problem says that $Ax=b$ got unique solution, so I've tried by getting rid of $A$ by using the inverse matrix but it doesn't work sice I don't know $A$.
- Since the constant matrix is $\begin{pmatrix}2\\1\\1\end{pmatrix}$ for both systems, I've tried $ABx = Ax$ but that also doesn't work for me.
Thanks in advance for your help and sorry for my bad English.
Lucas