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Unformatted text preview: rtible and has determinant 0.
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4) (16 points) Find the least squares plane of best ﬁt (in R3 ) for the four points (1, 0, 0),
(0, 1, 0), (1, 1, 3), (1, 2, 6) and that passes through the origin.
Solution: Since the plane passes through the origin, its equation is z = ax + by . We want
a and b. The equation we want to try and solve is 10
0
0 1 a
0 1 1 b = 3 .
12
6
By the theory of least squares, we need to solve 10
0
1 0 1 1 0 1 a
1 0 1 1 0 =
0 1 1 2 1 1 b
0 1 1 2 3
12
6
which becomes 33
36 a
b = 9
15
1
which has solution
=
. The plane z = x + 2y is the plane of...
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This note was uploaded on 01/30/2014 for the course MATH 2940 taught by Professor Hui during the Fall '05 term at Cornell University (Engineering School).
 Fall '05
 HUI
 Linear Algebra, Algebra, Vectors

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