Level
2

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 $a+b+c?$