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Linear AlgebraChallengeRow Reduction & Rank

Row Reduction & Rank · Challenge problem

Let AA be the 5×55\times 5 matrix with entries aij=max⁡(i,j)a_{ij} = \max(i, j):

A=(1234522345333454444555555).A = \begin{pmatrix} 1 & 2 & 3 & 4 & 5 \\ 2 & 2 & 3 & 4 & 5 \\ 3 & 3 & 3 & 4 & 5 \\ 4 & 4 & 4 & 4 & 5 \\ 5 & 5 & 5 & 5 & 5 \end{pmatrix}.

Gaussian elimination without row exchanges is applied to AA. What is the fifth pivot?