Suppose $\Delta$ is some nice topological space, say compact, and Hausdorff. Let $A:\Delta \rightarrow \mathbb{R}^{m\times n}$ be a continuous $m\times n$ matrix valued map. Let $b\in \mathbb{R}^{m}$ be a fixed vector that belongs to the range of $A(\delta)$ for all $\delta\in \Delta$. Then we know that there is a unique solution $x_*(\delta)$ to the optimization problem $$ \left\{ \begin{array}{ll} \textrm{minimize}& \frac{1}{2}\|x\|^2\\ \textrm{subject to}& A(\delta) x=b. \end{array}\right. $$ Question: Is the map $\delta\mapsto x(\delta):\Delta \rightarrow \mathbb{R}^n$ continuous?