Chapter 5.4, Problem 14E

In the accompanying figure, we show the kernel and theimage of a linear transformation L from ${ℝ}^2$ to ${ℝ}^2$ , together with some vectors ${\stackrel{\to }{v}}_1,{\stackrel{\to }{w}}_1,{\stackrel{\to }{w}}_2,{\stackrel{\to }{w}}_3$ . We are told that $L\left({\stackrel{\to }{v}}_1\right)={\stackrel{\to }{w}}_1$ . For $i=1,2,3$ , find the vectors $L^{+}\left({\stackrel{\to }{w}}_i\right)$ , where $L^{+}$ is the pseudo inverse of L defined inExercise 13. Show your solutions in the figure, and explain how you found them.