Chapter 5.1, Problem 16E

Consider the vectors ${\stackrel{\to }{u}}_1=\left[\begin{array}{l}1/2\\ 1/2\\ 1/2\\ 1/2\end{array}\right],{\stackrel{\to }{u}}_2=\left[\begin{array}{l}1/2\\ 1/2\\ -1/2\\ -1/2\end{array}\right],{\stackrel{\to }{u}}_3=\left[\begin{array}{l}1/2\\ -1/2\\ 1/2\\ -1/2\end{array}\right]$ in ${ℝ}^4$ . Can you find a vector ${\stackrel{\to }{u}}_4$ in ${ℝ}^4$ such that the vectors ${\stackrel{\to }{u}}_1,{\stackrel{\to }{u}}_2,{\stackrel{\to }{u}}_3,{\stackrel{\to }{u}}_4$ areorthonormal? If so, how manysuch vectors are there?