Real life application of Gaussian Elimination I would normally use Gaussian Elimination to solve a linear system. If we have more unknowns than equations we end up with an infinite number of solutions. Are there any real life applications of these infinite solutions? I can think of solving puzzles like Sudoku but are there others?

One important application is this: Given the corner points of a convex hull $\{\mathbf v_1,\cdots,\mathbf v_m \}$ in $n$ dimensions, s.t. $m > n+1$ and a point $\mathbf c$ inside the convex hull, find an enclosing simplex of $\mathbf c$(of  size $r \le n+1$). To solve the the problem, one can find a solution to $\alpha_1 \mathbf v_1+\cdots+\alpha_m \mathbf v_m=\mathbf c$ and $\alpha_1+\cdots+\alpha_m=1$. Once the solution is found, one can  use the Carathéodory's theorem to reduce the number of non-zero ${\alpha_i}'s$ to $r$.
