Past exam of the year 1 of the computer science course of the University of Oxford / 2017 / Digital systems, linear algebra, introduction to formal proof / 6 / b / iv / Solution

Yes. Part (a) diagonalizes $G=B$, whose spectral radius is $3/8<1$. Thusand every initial error converges to zero. For the specified initial vector, solving $Ax=b$ gives $x=(1,-1{)}^T$ and $e_0=(-1,1{)}^T$. In fact,The special formula is not asserted for $n=0$, because the zero-eigenvalue component disappears only after the first step.