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Does every non-singular matrix have a LU decomposition after pivoting? Explain.

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quant-research
data-analyst
Technical

To answer this question, you should be comfortable with the concepts of matrix singularity, LU decomposition, and pivoting. Focus your explanation on how pivoting helps achieve LU decomposition for non-singular matrices, making use of the existence of the L and U matrices which represent the lower and upper triangular matrices respectively.

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