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b₁₁ = 20 b=C+DtP3 b₁₂ = b3=8 e2 P2 1 P1 e1 b₁₁ = 0 4₁=0 12 = 1 eA PA b = (0,8,8,20) p = Ca₁ + Da2 a2 = (0, 1, 3, 4) 2 a₁ = (1, 1, 1, 1) 13 = 3 14=4 Figure 4.9: Problems 1-11: The closest line C + Dt matches Ca₁ + Da₂ in R4. With b = ΑΤΑΞ 0,8,8,20 at t = 0,1,3,4, set up and solve the normal equations ATb. For the best straight line in Figure 4.9a, find its four heights pi and four errors e¿. What is the minimum value E = e² + e² + e² + e²? =

b₁₁ = 20 b=C+DtP3 b₁₂ = b3=8 e2 P2 1 P1 e1 b₁₁ = 0 4₁=0 12 = 1 eA PA b = (0,8,8,20) p = Ca₁ + Da2 a2 = (0, 1, 3, 4) 2 a₁ = (1, 1, 1, 1) 13 = 3 14=4 Figure 4.9: Problems 1-11: The closest line C + Dt matches Ca₁ + Da₂ in R4. With b = ΑΤΑΞ 0,8,8,20 at t = 0,1,3,4, set up and solve the normal equations ATb. For the best straight line in Figure 4.9a, find its four heights pi and four errors e¿. What is the minimum value E = e² + e² + e² + e²? =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Check that e = b − p = (−1,3, −5,3) is perpendicular to both columns of the same matrix A. What is the shortest distance ||e|| from 6 to the column space of A?
Transcribed Image Text:Check that e = b − p = (−1,3, −5,3) is perpendicular to both columns of the same matrix A. What is the shortest distance ||e|| from 6 to the column space of A?
b₁₁ = 20 b=C+DtP3 b₁₂ = b3=8 e2 P2 1 P1 e1 b₁₁ = 0 4₁=0 12 = 1 eA PA b = (0,8,8,20) p = Ca₁ + Da2 a2 = (0, 1, 3, 4) 2 a₁ = (1, 1, 1, 1) 13 = 3 14=4 Figure 4.9: Problems 1-11: The closest line C + Dt matches Ca₁ + Da₂ in R4. With b = ΑΤΑΞ 0,8,8,20 at t = 0,1,3,4, set up and solve the normal equations ATb. For the best straight line in Figure 4.9a, find its four heights pi and four errors e¿. What is the minimum value E = e² + e² + e² + e²? =
Transcribed Image Text:b₁₁ = 20 b=C+DtP3 b₁₂ = b3=8 e2 P2 1 P1 e1 b₁₁ = 0 4₁=0 12 = 1 eA PA b = (0,8,8,20) p = Ca₁ + Da2 a2 = (0, 1, 3, 4) 2 a₁ = (1, 1, 1, 1) 13 = 3 14=4 Figure 4.9: Problems 1-11: The closest line C + Dt matches Ca₁ + Da₂ in R4. With b = ΑΤΑΞ 0,8,8,20 at t = 0,1,3,4, set up and solve the normal equations ATb. For the best straight line in Figure 4.9a, find its four heights pi and four errors e¿. What is the minimum value E = e² + e² + e² + e²? =
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