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Solve Linear System
MediumNumPy Linear Algebra
Problem Statement
Solve a system of linear equations Ax = b.
Background
A linear system Ax = b can be solved using:
- np.linalg.solve(A, b) - direct solution
- np.linalg.inv(A) @ b - via inverse (less efficient)
Example: 2x + y = 5, x + 3y = 7 Matrix form: [[2,1],[1,3]] @ [x,y] = [5,7]
Your Task
Write a function solve_system(A, b) that solves the linear system.
Output Format
Return a dictionary with:
- "solution": Solution vector x (rounded to 2 decimals, as list)
- "verification": A @ x (should equal b, rounded to 2 decimals, as list)
- "is_correct": True if A @ x ≈ b
Example:
Input:
A = [[2, 1], [1, 3]], b = [5, 7]
Output:
{'solution': [1.6, 1.8], 'verification': [5.0, 7.0], 'is_correct': True}Reasoning:
2(1.6) + 1(1.8) = 5, 1(1.6) + 3(1.8) = 7
Constraints:
- A is square and invertible
- Round to 2 decimal places
Editor
Python 3.13.1
Test Results
0/0Run code to see test results.