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In Exercises 40 through 43, consider the problem of fitting a conic through m given points P1(x1, yı), . .., Pm (xm, Ym) in the plane; see Exercises 53 through 62 in Section 1.2. Recall that a conic is a curve in R² that can be described by an equation of the form f(x, y) = c1 +c2x + c3y + c4x² + c5x y + c6y² = 0, where at least one of the coefficients c; is nonzero. 40. Explain why fitting a conic through the points P1 (x1, y1), ..., Pm(xm, Ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the ker- nel of A defines a unique conic, since the equations f(x, y) = 0 and kf (x, y) = 0 describe the same conic. %3D

In Exercises 40 through 43, consider the problem of fitting a conic through m given points P1(x1, yı), . .., Pm (xm, Ym) in the plane; see Exercises 53 through 62 in Section 1.2. Recall that a conic is a curve in R² that can be described by an equation of the form f(x, y) = c1 +c2x + c3y + c4x² + c5x y + c6y² = 0, where at least one of the coefficients c; is nonzero. 40. Explain why fitting a conic through the points P1 (x1, y1), ..., Pm(xm, Ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the ker- nel of A defines a unique conic, since the equations f(x, y) = 0 and kf (x, y) = 0 describe the same conic. %3D

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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In Exercises 40 through 43, consider the problem of fitting a conic through m given points P1(x1, yı), ..., Pm (Xm, Ym) in the plane; see Exercises 53 through 62 in Section 1.2. Recall that a conic is a curve in R? that can be described by an equation of the form f(x, y) = С1 + c2х + сзу + с4x* + csxу + С6у? 3D 0, where at least one of the coefficients c; is nonzero. 40. Explain why fitting a conic through the points P1 (x1, yı), ..., Pm(Xm, Ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the ker- nel of A defines a unique conic, since the equations f (x, y) = 0 and kf (x, y) = 0 describe the same conic. %3D
Transcribed Image Text:In Exercises 40 through 43, consider the problem of fitting a conic through m given points P1(x1, yı), ..., Pm (Xm, Ym) in the plane; see Exercises 53 through 62 in Section 1.2. Recall that a conic is a curve in R? that can be described by an equation of the form f(x, y) = С1 + c2х + сзу + с4x* + csxу + С6у? 3D 0, where at least one of the coefficients c; is nonzero. 40. Explain why fitting a conic through the points P1 (x1, yı), ..., Pm(Xm, Ym) amounts to finding the kernel of an m × 6 matrix A. Give the entries of the ith row of A. Note that a one-dimensional subspace of the ker- nel of A defines a unique conic, since the equations f (x, y) = 0 and kf (x, y) = 0 describe the same conic. %3D
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