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Linear Algebra Solutions 25

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

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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 = fl fl fl fl 45 18 73 30 fl fl fl fl fl fl fl fl 11 18 18 30 fl
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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...
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