Let a square $n\times n$ real matrix ${\bf A}$ and two vectors ${\bf x}$ and ${\bf b}$ of length $n$, such that $${\bf A}{\bf x}={\bf b}.$$ Solving for ${\bf x}$ through standard G …

I am sorry for spamming MO with questions I have not thought about for more than 3 hours, but currently I am quite busy with preparing a talk on representations of $S_n$, and I don …