Howard Elman who set this problem says:

> 	The assertion for part (b) should be for k=1, which then leads to a bound on
> 	||r_1|| using parts (c) and (d) below that.
>
> 	The proper way to use this result to complete the proof of Proposition 4.3
> 	is to observe that the analysis of parts (b)-(d) actually establishes a
> 	bound on the quantity ||p_1(F)||^2 where p_1 is the optimal polynomial
> 	obtained in going from step 0 to step 1 in GMRES.
>
> 	This can then be used to bound ||r_k||/||r_0|| as follows:  with p_k the
> 	optimal polynomial obtained at step k, this ratio is bounded by
>
> 	   ||p_k(F)|| \le ||p_1(F)^k|| \le ||p_1(F)||^k .
>
> 	The expression on the right here is bounded via the second paragraph
> 	above, and this gives the bound on ||r_k|| in Proposition 4.3.