Find a least squares solution of Ax=b by constructing and solving the normal equations. A=[(3,1),(1,1),(1,4)], b[(1),(1),(1)] bar(x)=?

nitraiddQ

nitraiddQ

Answered question

2020-10-18

Find a least squares solution of Ax=b by constructing and solving the normal equations.
A=[311114],b[111]
x=?

Answer & Explanation

nitruraviX

nitruraviX

Skilled2020-10-19Added 101 answers

A=[311114],b[111] 
ATAx=AT b. Compute the relevant matrices. 
ATA=[311114][311114]=[118818] 
ATb=[311114][111]=[56] 


Solve [118818]x=[56]
[11858186][31018186] 
[11036188] 
[110304210] 
[11030215] 


x1+10x2=3 
21x2=5 
x2=521,x1=11321 
x=[11321521]

Jeffrey Jordon

Jeffrey Jordon

Expert2021-11-03Added 2605 answers

Answer is given below (on video)

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