  In this note, following suggestions by Tao, we extend the randomized
algorithm for linear equations over prime fields by Raghavendra to a randomized
algorithm for linear equations over the reals. We also show that the algorithm
can be parallelized to solve a system of linear equations $A x = b$ with a
regular $n \times n$ matrix $A$ in time $O(n^2)$, with probability one. Note
that we do not assume that $A$ is symmetric.
