Inconsistent results with np.linalg.solve on nearly singular matrices in NumPy 1.25
I'm confused about I'm a bit lost with I'm working on solving a system of linear equations using `np.linalg.solve`, but I'm working with inconsistent results when the coefficient matrix is nearly singular. For example, given the following code: ```python import numpy as np A = np.array([[1, 2, 3], [2, 4, 6], [1, 1, 1]]) # Nearly singular matrix B = np.array([1, 2, 3]) try: x = np.linalg.solve(A, B) print(x) except np.linalg.LinAlgError as e: print(f'behavior: {e}') ``` When I run this, I sometimes get unexpected results. The output doesn't seem to match what I expect based on manual calculations, and on occasion, I receive the `LinAlgError` indicating that the matrix is singular. I’ve tried to check the condition number of the matrix with `np.linalg.cond(A)` and found that it’s quite high, suggesting numerical instability. I’ve also attempted to use `np.linalg.pinv(A)` to compute the pseudo-inverse as a fallback: ```python x_pinv = np.linalg.pinv(A).dot(B) print(x_pinv) ``` However, the results differ significantly from what I anticipated. I would appreciate any insights on how to handle nearly singular matrices effectively in NumPy, especially ways to stabilize the solution or validate the results. Are there best practices or alternative methods that I should consider? I've been using Python for about a year now. Any advice would be much appreciated.