Let a 26 47t consider nbspthe floating-point algorithm

Question

(1) Let a = (2.6, 4.7)^T. Consider  the floating-point algorithm with  3 digit rounding.

a) Compute fl(a^Ta).

b) Compute fl(aa^t).

c) Compute the Householder matrix Q generated by a as a 2x2 array. (Remember to round each computation to 3 digit)

d) Compute QTQ and ||Q^TQ - I||, here ||·|| is the matrix norm induced by the vector 1-norm.