SciPy - Linear Algebra (scipy.linalg)
Given a matrix A, you want to compute its determinant using LU decomposition. Which expression correctly computes det(A)?
Given a matrix A, you want to compute its determinant using LU decomposition. Which expression correctly computes det(A)?
hard📝 Application Q9 of 15
Step-by-Step Solution
Solution:
Step 1: Recall determinant properties in LU decomposition
LU decomposition gives PA = LU, so det(P)*det(A) = det(L)*det(U).Step 2: Use determinant facts
Since L is lower triangular with unit diagonal, det(L) = 1. So det(A) = det(P) * det(U), and det(U) is product of U's diagonal elements.Final Answer:
det(A) = det(P) * product of diagonal elements of U -> Option BQuick Check:
det(A) = det(P) * ∏ diag(U) [OK]
Quick Trick: Determinant = det(P) times product of U diagonal [OK]
Common Mistakes:
MISTAKES- Multiplying diagonal elements of L and U
- Adding determinants instead of multiplying
- Ignoring permutation matrix determinant
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