# Compute Row Space Of 2-By-3 Matrix

Level pending

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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