implementing np.linalg.solve giving unexpected results for underdetermined systems in NumPy 1.24.2
I'm sure I'm missing something obvious here, but I'm trying to solve a system of linear equations using `np.linalg.solve`, but I'm working with unexpected results when the system is underdetermined. For example, when I try to solve the following equations: ```python import numpy as np A = np.array([[1, 2], [2, 4]]) # This is an underdetermined system B = np.array([5, 10]) x = np.linalg.solve(A, B) ``` I expect to get a solution with infinite possibilities, but instead, I'm getting a `LinAlgError` indicating that the matrix is singular. I've tried using `np.linalg.lstsq` as a workaround: ```python x_lstsq, residuals, rank, s = np.linalg.lstsq(A, B, rcond=None) ``` This does give me a solution, but I'm unsure if it's the best representation or if I'm losing important information about the solution space. Is there a recommended way to handle such cases where the system is underdetermined? Should I be using a different method or adjusting the matrix in some way before applying `np.linalg.solve`? I would appreciate any insights into how to better handle these situations in NumPy 1.24.2. I'm working on a application that needs to handle this. What's the best practice here? Any ideas what could be causing this? The stack includes Python and several other technologies. Thanks for taking the time to read this!