3. Consider computing a basis for the Krylov sub-space Kk (A, r.). (a) In forming a basis for Kx (A, r.), describe one reason why the most obvious choice of {ro, Aro,..., Ak-ro} is not the most appropriate one numerically. [2/6] (b) Recall that a proper basis was found using Arnoldi process, which is a modified Gram-Schmidt procedure and can be compactly represented as = (I - Q&Q) Aqk, z/|2| Z= qk+1 = where Qk = [91]... | qk], are previous Arnoldi vectors such that Q AQk is upper Hessenberg for all k. Find the missing blocks in the recursive formula below only in terms of Qk, A. qk and z. Hk k-1 Hk+1,6 = ? ? ER(k+1)xk ? Note that the bottom right block is 1 x 1, i.e., a scalar value. [4/6] 3. Consider computing a basis for the Krylov sub-space Kk (A, r.). (a) In forming a basis for Kx (A, r.), describe one reason why the most obvious choice of {ro, Aro,..., Ak-ro} is not the most appropriate one numerically. [2/6] (b) Recall that a proper basis was found using Arnoldi process, which is a modified Gram-Schmidt procedure and can be compactly represented as = (I - Q&Q) Aqk, z/|2| Z= qk+1 = where Qk = [91]... | qk], are previous Arnoldi vectors such that Q AQk is upper Hessenberg for all k. Find the missing blocks in the recursive formula below only in terms of Qk, A. qk and z. Hk k-1 Hk+1,6 = ? ? ER(k+1)xk ? Note that the bottom right block is 1 x 1, i.e., a scalar value. [4/6]