A) Find an orthonormal set q1, q2, q3 for which q1,q2 span the column space A [1 1; 2, -1; -2,4] (this is a 3x2 matrix).
B) Which fundamental subspace contains q3?
C) What is the least-squares solution of Ax=b if b=[1 2 7]T?
The Attempt at a Solution
A) So I figured out q1, q2, and q3 using Gram-Schmidt process. These are q1 = [1/3 2/3 -2/3]T, q2 = [2/3 1/3 2/3]T, and q3 = +-[-2/3 2/3 1/3]T
B) Don't know how to determine this
C) For the least square, since they are orthonormal sets, I used the formula x= [q1Tb; q2Tb] However, I'm not getting the right answer. In addition, I tried doing it the long way using the formula x=(ATA)-1ATb, I'm getting even different numbers... Please help!