Question

3. Find the best straight-line fit (least squares) to the measurements t -2, b 4 at at t =-1 b 1 at t0 b 0 at t = 2. Then find the projection p of 3 b 0 onto the column space of A = 1 10 1 2

Answer 1

solution - = Given b=4 at to-2, b=1 at roo, 6-3 at tori, bo at t=2 best fit line be Let the equation of the the form b= c+ Dt Then we can corire. 147 Ft -27 l -1 . o-W To find the best least square solution [87. wе gе px 0 e@uction АТАХ - АТЬ now Pi -2 A -

ΑΤΑ sriui 7 - +1 +0+27 Titititi htltotu totų & Atb . .] :] 14+3+1+0

ATA X=Atb X = (ATA)'Atb. augmented matrin consider the Apply Red R2 Apply R, (-) R, Apply R2-4R, i .-1 10 H - 36 0 -4 -) (+) 12 (t) 0 35 4 7 C APPLY R si -4 0 -17 Apply RoRitare

「。 ks 7 le s s」 1-10-1 oass ico's : 7 x = art"] ATS :::(( : [] 15 ce & D-

Hence the best line fit is. | b = %s 上 Beaction ol be (4.3.yo) on to ha , column space of A is P = AX P- 1 Alt2 *][12] 5 60*36 3s %%%%