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 2020-10-18 Answered
Find a least squares solution of Ax=b by constructing and solving the normal equations.
A=[311114],b[111]
x=?
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nitruraviX
Answered 2020-10-19 Author has 101 answers
Step 1
We have to find the least square solution of Ax = B, by constructing the normal equations, where
A=[311114],b[111]
The set of solutions of the non-empty solutions is given by
ATAx=AT b.To solve this normal equations, we first compute the relevant matrices.
ATA=[311114][311114]=[118818]
ATb=[311114][111]=[56]
Step 2
Now, we need to solve [118818]x=[56].
The augmented matrix is given by
[11858186][31018186]
[11036188]
[110304210]
[11030215]
Step 3
From the final matrix, we get the following equations x1+10x2=3
21x2=5
x2=521,x1=11321
x=[11321521]
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Jeffrey Jordon
Answered 2021-11-03 Author has 2313 answers

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