Compute Row Space Of 2-By-3 Matrix

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Consider the matrix

\[B= \begin{pmatrix} 8 & -5 & 2 \\0 & 2 & 1 \end{pmatrix}.\]

Note that the column space \(C(B)\) is just \(\mathbb{R}^2\), since the first two columns are linearly independent. The row space \(R(B)\) has equation \(ax+by+cz = 0\), where \(a,b,c\in \mathbb{Z}, a>0,\) and \(\gcd(a,b,c) =1\). What is \(a+b+c?\)

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