Exercise 4

Perform Gram-Schmidt on each of these bases for $\mathbb{R}^{2}$.

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

Then turn those orthogonal bases into orthonormal bases.