👀 Views: 4 💬 Answers: 1 📅 Created: 2025-06-06

numpy linear-algebra python

I'm trying to use `np.linalg.solve` to solve a system of equations represented by a non-square matrix, but I'm receiving a `LinAlgError`. I understand that `np.linalg.solve` is meant for square matrices, but I’m unsure how to handle my specific scenario. I have the following code snippet that raises the error: ```python import numpy as np # Coefficients of my equations A = np.array([[2, 1], [1, 1], [1, 3]]) # Non-square matrix (3x2) B = np.array([4, 2, 5]) # Right-hand side (3x1) # Attempt to solve the equations x = np.linalg.solve(A, B) # This raises LinAlgError ``` The error message I receive is: `LinAlgError: Last 2 dimensions of the array must be square`. I am aware that for non-square systems, I should use `np.linalg.lstsq`, but I'm confused about how to apply it correctly. I've tried the following to use `np.linalg.lstsq`, but I'm not sure if I'm handling the outputs correctly: ```python x, residuals, rank, s = np.linalg.lstsq(A, B, rcond=None) print('Solution:', x) print('Residuals:', residuals) ``` When I run this, the output is a solution array, but the `residuals` array is empty, and I'm not entirely sure what that implies. Could someone clarify how to properly interpret the output of `np.linalg.lstsq` in this context? Also, are there any best practices for handling such scenarios with non-square matrices? Any insights into why the residuals might be empty would also be appreciated.