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## Homework Statement

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}?

## Homework Equations

Gram-Schmidt

## 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= [q1

^{T}b; q2

^{T}b] However, I'm not getting the right answer. In addition, I tried doing it the long way using the formula x=(A

^{T}A)

^{-1}A

^{T}b, I'm getting even different numbers... Please help!