I need to proof the following: When a homogeneous linear system has more variables than equations it has infinite solutions. I don't know where to start! Thank you for your help
2026-03-26 20:38:30.1774557510
Homogeneous linear system with more variables than equations
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At first remember that if $x$ is a solution of an homogeneous linear system, than also $\alpha x$ is (with $\alpha \in \mathbf{R}$).
Then for example the Gram Schmidt process describes how to find many orthogonal solutions, and you can exploit it to prove it.