Suppose that we have vectors $\vec{a}$, $\vec{b}$ and $\vec{x}_k$ which are $2\times1$ in dimension. I want to solve for $\vec{a}$ in the following:
\begin{equation} \sum_{k=1}^N(\vec{a}^T\vec{x}_k)\vec{x}_k = \sum_{k=1}^N(\vec{b}^T\vec{x}_k)\vec{x}_k \end{equation}
Here is my attempt: \begin{equation} \sum_{k=1}^N\vec{a}^T\vec{x}_k = \frac{\sum_{k=1}^N(\vec{b}^T\vec{x}_k)\vec{x}_k}{\sum_{k=1}^N\vec{x}_k} \end{equation}
I'm stuck here, I'm not sure how to bring the $\vec{a}$ out of this.