Prelim 2 [Solutions]

# Solution since the plane passes through the origin

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Unformatted text preview: rtible and has determinant 0. uv 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).

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