Exercise 5

Perform the Gram-Schmidt process on each of these bases for $\mathbb{R}^{3}$.

• (a)  $\langle\begin{pmatrix}2\\ 2\\ 2\end{pmatrix},\begin{pmatrix}1\\ 0\\ -1\end{pmatrix},\begin{pmatrix}0\\ 3\\ 1\end{pmatrix}\rangle$     (b)  $\langle\begin{pmatrix}1\\ -1\\ 0\end{pmatrix},\begin{pmatrix}0\\ 1\\ 0\end{pmatrix},\begin{pmatrix}2\\ 3\\ 1\end{pmatrix}\rangle$

Then turn those orthogonal bases into orthonormal bases.