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Question 2.7.23: Find a 4 by 4 permutation matrix (call it A) that needs 3 ro...

Find a 4 by 4 permutation matrix (call it A) that needs 3 row exchanges to reach the end of elimination. For this matrix, what are its factors P, L, and U?

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A=\left[ \begin{matrix} 0 & 0 & 0 & 1 \\ 1 & 0 & 0 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \end{matrix} \right] =P and L=U=I.

This cyclic P exchanges rows 1-2 then rows 2-3 then rows 3-4.

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