Page 849 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition
P. 849
(a) Show that if the nine points for , 2, 3, …, 9 lie on this surface, and if they determine uniquely the
equation of this surface, then its equation can be written in determinant form as
(b) Use the result in part (a) to determine the equation of the quadric surface that passes through the points (1, 2, 3), (2, 1,
7), (0, 4, 6), (3, −1, 4), (3, 0, 11), (−1, 5, 8),(9, −8, 3), (4, 5, 3), and (−2, 6, 10).
(c) Use the methods of Section 9.7 to identify the resulting surface in part (b).
T2.
(a) A hyperplane in the n-dimensional Euclidean space has an equation of the form
where , , 2, 3, …, , are constants, not all zero, and , , 2, 3, …, n, are variable
for which
A point
lies on this hyperplane if
Given that the n points , , 2, 3, …, n, lie on this hyperplane and that th
uniquely determine the equation of the hyperplane, showthat the equation of the hyperplane
can be written in determinant form as
(b) Determine the equation of the hyperplane in that goes through the following nine points:
