Is it possible to solve for a matrix $ m $ satisfying $ m\cdot x=b $, given the vectors $ x $ and $ b $?

Question

At first I thought it should be LinearSolve, which however turns out aiming at x, given m and b in m.x == b.

Answer 1

Yes, but the solution is not unique. In some sense, the optimal solution is the following rank-one matrix:

m = KroneckerProduct[b, x/x.x]