Linear Algebra Solutions 25

Linear Algebra Solutions 25 - 30 f f f f = 36 6 = 6 y = f f...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
The last row reveals inconsistency. The system in matrix form is AX = B , where A = 1 2 1 1 3 5 , X = x y , B = 4 5 12 . The normal equations are given by the matrix equation A t AX = A t B. Now A t A = 1 1 3 2 1 5 1 2 1 1 3 5 = 11 18 18 30 A t B = 1 1 3 2 1 5 4 5 12 = 45 73 . Hence the normal equations are 11 x + 18 y = 45 18 x + 30 y = 73 . These may be solved, for example, by Cramer’s rule: x = f f f f 45 18 73 30 f f f f f f f f 11 18 18
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 30 f f f f = 36 6 = 6 y = f f f f 11 45 18 73 f f f f f f f f 11 18 18 30 f f f f =-7 6 . 23. Substituting the coordinates of the Fve points into the parabola equation gives the following equations: a = 0 a + b + c = a + 2 b + 4 c =-1 a + 3 b + 9 c = 4 a + 4 b + 16 c = 8 . 28...
View Full Document

Ask a homework question - tutors are online