In Exercise 40 through 43, consider the problem of fitting a conic through given points in the plane; see Exercise 53 through 62 in section 1.2. Recall that a conic is a curve in that can be described by an equation of the form , where at least one of the coefficients is non zero.
40. Explain why fitting a conic through the points amounts to finding the kernel of an matrix . Give the entries of the row of .
Note that a one-dimensional subspace of the kernel of defines a unique conic, since the equations and describe the same conic.
Thus, the entries for row are .
A conic is a curve in that can be described by an equation of the form , where at least one of the coefficients is non-zero.
To fit a conic through the points is equivalent to find the kernel of an of matrix and also these are solution to the equation.
Thus, the row have entries as follows:
Hence, the entries for row are .
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