SciPy - Linear Algebra (scipy.linalg)
You have a matrix A and want to solve Ax = b using LU decomposition. Which step correctly describes how to find x?
You have a matrix A and want to solve Ax = b using LU decomposition. Which step correctly describes how to find x?
hard📝 Application Q8 of 15
Step-by-Step Solution
Solution:
Step 1: Understand LU decomposition for solving Ax = b
LU decomposition gives P, L, U such that PA = LU. To solve Ax = b, rewrite as LUx = Pb.Step 2: Solve system in two steps
First solve Ly = Pb for y, then solve Ux = y for x.Final Answer:
Decompose A into P, L, U; solve Ly = Pb; then solve Ux = y -> Option DQuick Check:
Solving Ax=b via LU: Ly=Pb, then Ux=y [OK]
Quick Trick: Solve Ly=Pb first, then Ux=y to find x [OK]
Common Mistakes:
MISTAKES- Ignoring permutation matrix P in Pb
- Solving equations in wrong order
- Confusing variables y and x
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