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Linear AlgebraChallengeRow Reduction & Rank

Row Reduction & Rank · Challenge problem

A 3×43\times 4 matrix AA has reduced row echelon form

R=(120−100130000).R = \begin{pmatrix} 1 & 2 & 0 & -1 \\ 0 & 0 & 1 & 3 \\ 0 & 0 & 0 & 0 \end{pmatrix}.

The first column of AA is (1,2,3)(1, 2, 3) and the third column is (1,1,2)(1, 1, 2). Find the sum of the three entries in the fourth column of AA.