np.linalg.solve raises LinAlgError for singular matrix despite expected behavior
I'm not sure how to approach After trying multiple solutions online, I still can't figure this out... I'm relatively new to this, so bear with me... I'm trying to solve a system of linear equations using `np.linalg.solve`, but I'm working with a `LinAlgError` indicating that the matrix is singular, even though I expect it to return a solution based on the input values. Here's the code snippet I'm working with: ```python import numpy as np A = np.array([[1, 2, 3], [2, 4, 6], [3, 6, 9]]) # This should be singular B = np.array([1, 2, 3]) try: x = np.linalg.solve(A, B) except np.linalg.LinAlgError as e: print(f"LinAlgError: {e}") ``` When I run this, I get the following behavior: ``` LinAlgError: Singular matrix ``` From what I understand, the matrix `A` is singular since its rows are linearly dependent. However, I also expected that `np.linalg.lstsq` would provide an alternate way to solve this system. I've tried using `np.linalg.lstsq` as follows: ```python x_lstsq, residuals, rank, s = np.linalg.lstsq(A, B, rcond=None) print(x_lstsq) ``` But I still get unexpected results, as the solution does not seem to align with what I originally anticipated. This leads me to question whether I'm correctly interpreting the output from `np.linalg.lstsq`. Am I missing something in my implementation or understanding of how to handle singular matrices in NumPy? Also, what would be the best practice for handling such cases in real-world applications? I'm using NumPy version `1.23.5`. I recently upgraded to Python LTS. I appreciate any insights! How would you solve this?