Simultaneous confidence interval task

Question

The task is to find simultaneous confidence intervals for $\mu_1$ and $\mu_2$. We have given matrix:

then mean matrix:

Also, we see that p=2, n=3. The solution:

Here $\mathbb{S}$ is empirical covariance matrix. My question, why vectors $\overrightarrow{a_1}^T=(1,0)$ and $\overrightarrow{a_2}^T=(0,1)$? Or these vectors should be given in the task?