[Solved] What are the three matrices obtained from LU decomposition of a square matrix A? — Ans: Lower triangular matrix L, Upper triangular matrix U, and Permutation matrix P | SciPy

SciPy - Linear Algebra (scipy.linalg)

What are the three matrices obtained from LU decomposition of a square matrix A?

ADiagonal matrix D, Orthogonal matrix Q, and Permutation matrix P

BUpper triangular matrix U, Diagonal matrix D, and Identity matrix I

CSymmetric matrix S, Diagonal matrix D, and Orthogonal matrix Q

DLower triangular matrix L, Upper triangular matrix U, and Permutation matrix P

Step-by-Step Solution

Solution:

Step 1: Understand LU decomposition output
LU decomposition factorizes a matrix A into three matrices: L (lower triangular), U (upper triangular), and P (permutation matrix) to handle row exchanges.
Step 2: Match matrices with options
Only Lower triangular matrix L, Upper triangular matrix U, and Permutation matrix P correctly lists L, U, and P matrices as output of LU decomposition.
Final Answer:
Lower triangular matrix L, Upper triangular matrix U, and Permutation matrix P -> Option D
Quick Check:
LU decomposition matrices = L, U, P [OK]

Quick Trick: LU decomposition always returns L, U, and P matrices [OK]

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What are the three matrices obtained from LU decomposition of a square matrix A?