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Proof: For every invertible matrix $A$ there is a permutation matrix $P$ and an invertible upper triangular matrix $R$ and $R'$, such that $A=R'PR$...

Can someone give me a hint? I dont even know where to start

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  • $\begingroup$ en.wikipedia.org/wiki/LU_decomposition $\endgroup$
    – Dmitry
    Oct 18, 2021 at 11:46
  • $\begingroup$ Are you sure you want A=R'PR Can you show me the excercise? $\endgroup$
    – Jam
    Oct 18, 2021 at 12:47
  • $\begingroup$ @Jam i am....i would show you but its in german....but i nearly translate word by word so should be correct $\endgroup$ Oct 18, 2021 at 13:04
  • $\begingroup$ @Dmitry i know lu decomp....but does that apply`? $\endgroup$ Oct 18, 2021 at 13:04
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    $\begingroup$ math.stackexchange.com/questions/758968/… $\endgroup$
    – Jam
    Oct 18, 2021 at 13:17

1 Answer 1

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Hint: If you matrix has as $a_{11}$ entry zero permute the row with a non zero row. Now start doing gauss ellimination. Keep all the accounting in matrix forms. Remember multiplying a matrix from the left gives sou row combinations as gauss ellimination does. Multiplying from right gives you collumn combinations. Can you do a similar method to get your result? (A is invertible so its not a zero matrix and a diagonal matrix is also an upper traingular) .

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