Let $n\in \mathbb{N}$. Let $A\in {\mathbb{R}}^{n\times n}$ be a "given" square, nonsingular matrix. Let $\overrightarrow{b}\in {\mathbb{R}}^n$ be a "given" vector. Then, the square linear-systems problem (AKA the NLSP) is to find an unknown vector $\overrightarrow{x}\in {\mathbb{R}}^n$ such that
$A\cdot \overrightarrow{x}=\overrightarrow{b}$

• Note that this is a backwards problem.