Find a least-squares solution of Ax=b by (a) constructing the

uneskovogl5

uneskovogl5

Answered question

2021-11-20

Find a least-squares solution of Ax=b by (a) constructing the normal equations for x^ and (b) solving for x^
A=[212023],b=[581]

Answer & Explanation

Sevensis1977

Sevensis1977

Beginner2021-11-21Added 15 answers

We are aware that every least squares solution to x=b satisfies the equation ATAx=ATb. hence, find out first ATA,ATb
ATA=[222103][212023]=[128810]
ATb=[222103][581]=[242]
The equation ATAx=ATb becomes.
[128810][x1x2]=[242]
The augmented matrix for ATAx=ATb to solve this sytem
[128248102]
Apply row operations to this system's solution
[128248102][104013]
the augmented matrix's answer.
x1=4, x2=3
The typical least squares answer for Ax=b
x^=[43]

Jeffrey Jordon

Jeffrey Jordon

Expert2022-01-30Added 2605 answers

Answer is given below (on video)

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