Compute Row Space Of 2-By-3 Matrix

Level 2

Consider the matrix

B=(852021).B= \begin{pmatrix} 8 & -5 & 2 \\0 & 2 & 1 \end{pmatrix}.

Note that the column space C(B)C(B) is just R2\mathbb{R}^2, since the first two columns are linearly independent. The row space R(B)R(B) has equation ax+by+cz=0ax+by+cz = 0, where a,b,cZ,a>0,a,b,c\in \mathbb{Z}, a>0, and gcd(a,b,c)=1\gcd(a,b,c) =1. What is a+b+c?a+b+c?

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