hw13.solutions

The projection is y u2 y u3 1 14 1 y u1 u1 u1 u2

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Unformatted text preview: , u3 , u4 #6. The projection is y · u1 y · u2 3 5 u1 + u2 = − u1 + u2 = (6, 4, 1) u1 · u1 u2 · u2 2 2 #10. The projection is y · u2 y · u3 1 14 1 y · u1 u1 + ++ = u1 + u2 − u3 = (5, 2, 3, 6). u1 · u1 u2 · u2 u3 · u3 3 3 3 The perpendicular vector is (3, 4, 5, 6) − (5, 2, 3, 6) = (−2, 2, 2, 0). 1 #14. The closest point in the projection z · v1 z · v2 1 v1 + v2 = v1 + 0v2 = (1, 0, −1/2, −3/2). v1 · v1 v2 · v2 2 ˆ #16. The projection is ˆ = (−1, −5, −3, 9) and the distance is ||y − y || = √y |(| − 4,...
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