Problem
Using $\beta_k = \frac{r_k^TAp_{k-1}}{p_{k-1}^TAp_{k-1}}$ verify that $ span[r_0, ..., r_k] = span[Ar_0, ..., A^kr_0] $ and $span[p_0, ..., p_k] = span[Ar_0, ..., A^kr_0] $ hold for k = 1
Solution
2) To show the other direction we subsiture $r_0$ with $- p_0$ and solve in the same fashion