Exercise 4.1.27

The lines $3x+y=b_1$ and $6x+2y=b_2$ are parallel. They are the same line if $b_2=2b_1$. In that case $\left(b_1,b_2\right)$ is perpendicular to $(-2,1)$. The nullspace of the 2 by 2 matrix is the line $3x+y=0$. One particular vector in the nullspace is $(-1,3)$.