(Solved):   \( \begin{array}{l}\text { An orthogonal basis for the column space of matrix } \\ \text { ...

 

\( \begin{array}{l}\text { An orthogonal basis for the column space of matrix } \\ \text { A is }\left\{v_{1}, v_{2}, v_{3}\right\} \text {. Use this orthogonal basis to find } \\ \text { a QR factorization of matrix A. }\end{array} \quad A=\left[\begin{array}{rrr}1 & 3 & 6 \\ -1 & -4 & 1 \\ 0 & 3 & 3 \\ 1 & 4 & 3 \\ 1 & 5 & 8\end{array}\right], v_{1}=\left[\begin{array}{r}1 \\ -1 \\ 0 \\ 1\end{array}\right], v_{2}=\left[\begin{array}{r}-1 \\ 0 \\ 1\end{array}\right] \) \[ \mathrm{Q}=\mathrm{R}= \] (Type exact answers, using radicals as needed.)