Singular Values & the SVD · Medium problem

Let $A = \begin{pmatrix}1 & 1\\1 & 1\\1 & -1\end{pmatrix}$, and let $u_1 = (a, b, c)^{T}$ be its first left singular vector (for the largest singular value), with $a > 0$. Find $a + b + c$. Give your answer in simplest radical form.