Exercise 4.1.14

$Ax=B\hat{x}$ means that $\left[\begin{array}{cc}A\hfill & B\hfill \end{array}\right]\left[\begin{array}{c}\hfill x\\ \hfill -\hat{x}\end{array}\right]=0$. Three homogeneous equations (zero right hand sides) in four unknowns always have a nonzero solution. Here $x=(3,1)$ and $\hat{x}=(1,0)$ and $Ax=B\hat{x}=(5,6,5)$ is in both column spaces. Two planes in $R^3$ must share a line.