I have a linear system with 1 more unknown than equation. My questions are:
If I express this equation in matrix form, what 'result' will a computer spit out when solving it (say, with Maple and the command LinearSolve)? Will it choose one free variable on its own, and express all others in terms of this? (I have no specific data to test it myself, and I want a general answer as well, if one exists).
What if I want the solution vector $x$ which has the smallest Euclidean norm. How would I impose this restriction? How would I make a computer give me this specific solution? Are there infinitely many solutions in this case too, or does this condition remove that arbitrariness one has with an extra unknown and gives exactly one solution?
When expressed in matrix form, the linear system is tridiagonal, if that has any relevance.