2. Let $H=\operatorname(span}\left\{u_{1}, u_{2}, u_{3} ight\}$ and $K=\operatornamespan}\left\{v_{1}, v_{2}, v_{3} ight\}$ where $$ u_{1}=\left[\begin{array}{c} 1 2 0 -1 \end{array} ight), u_{2}=\left[\begin{array}{c} 0 21 -1 1 \end{array} ight], u_{3}=\left[\begin{array}{c} 3 4 1 -4 \end{array} ight] \text { and } v_{1}=\left[\begin{array}{c} - 2 1 -2 -1 3 \end{array} ight], v_{2}=\left[\begin{array}{c} 2 3 2 -6 \end{array} ight], v_{3}=\left[\begin{array}{c} -1 6 - 2 \end{array} ight] $$ Find the base for $H, K$, and $H+K .$ Solution: CS.JG. 108