= Solution
The first column has norm two, giving $q_1=(1,-1,1,-1)^T/2$. Its inner products with the second and third columns are both one. Subtracting $q_1$ from the second column leaves $(3,3,3,3)^T/2$, of norm three, so $q_2=(1,1,1,1)^T/2$. The inner product of $q_2$ with the third column is one. Subtracting $q_1+q_2$ from that column leaves $(1,1,-1,-1)^T$, of norm two. Thus the <Gram-Schmidt process> gives
$$
\boxed{Q=\frac12\begin{pmatrix}1&1&1\\-1&1&1\\1&1&-1\\-1&1&-1\end{pmatrix},\qquad R=\begin{pmatrix}2&1&1\\0&3&1\\0&0&2\end{pmatrix}.}
$$
The columns of $Q$ have unit norm and pairwise zero <inner products>, so $Q^TQ=I_3$. Direct multiplication verifies $QR=A$.
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