Please help me with this HW question. (Might need to unfold it)

5.5 Orthoganolizing vectors. Suppose that o. and b are any n-vectors. Show that we can always nd a scalar 1r so that (o. Tb) J. b, and that 1/ is unique if b ; 0. (Give a formula for the scalar 7.) In other words, we can always subtract a multiple of a vector from another one, so that the result is orthogonal to the original vector. The orthogonalizat ion step in the GramSchmidt algorithm is an application of this. Question 1. Continuing 5.5 from the textbook, above. Let a, b, and 7 be as in Problem 5.5 from the textbook. Show that 71) is the closest point to a out of all points in the subspace span({b}). That is, show that if y e span({t}), then Ila tn 2 Ha - vbll