In 2B The General Linear-Systems Problem, we will see we have three options for solution type.

1. Unique solution: Given $\overrightarrow{b}\in \text{Rng}(f)$ and $A$ must be full-rank^[1] (full column rank).
2. Nonunique solution: Given $\overrightarrow{b}\in \text{Rng}(f)$ and $A$ rank deficient (aka $A$ is not full rank & not one-to-one).
3. No solution: Given $\overrightarrow{b}\in \text{Codomain}(f)={\mathbb{R}}^m$ but $\overrightarrow{b}\notin \text{Rng}(f)$. In this case, the GLSP has no solution but we can think about minimizing the distance between $\text{Rng}(f)$ and given $\overrightarrow{b}$.

• Problem 4: 3 The Full-Rank Least-Squares Problem
• Problem 6: RDLSP