Exercise 2.3.8

Follow the steps on page 130 of the Gram-Schmidt with pivoting, we see that the first $q_1$ will be chosen by column 2, and the second $q_2$ will be chosen by column 3, i.e. $q_1=\frac{1}{A_1}\left[\begin{array}{c}\hfill 1\hfill \\ \hfill 1+𝜖\hfill \\ \hfill 1\hfill \end{array}\right]$, $q_2=\frac{1}{A_2}\left[\begin{array}{c}\hfill 1-\frac{1}{A_1^2}\hfill \\ \hfill -\frac{1+𝜖}{A_1^2}\hfill \\ \hfill -\frac{1}{A_1^2}\hfill \end{array}\right]$, with $A_1,A_2$ being the normalization factors for each vector.