(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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}?

2. Relevant equations

Gram-Schmidt

3. 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!

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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# Finding orthonormal set using Gram-Schmidt and least squares

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