Verify that {u₁,u₂} is an orthogonal set, and then find theorthogonal projection of y onto Span{₁,₂}.2CHHO3 U₁ 6= 2- 30y =7- 6To verify that {u₁,u₂} is an orthogonal set, find u₁ • U₂.U₁ U₂ = 0 (Simplify your answer.)The projection of y onto Span{₁,₂} is(Simplify your answers.)

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Answered: Verify that {u₁,u₂} is an orthogonal…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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2. In a dance performance, four dancers form a diamond with vertices A(2, 0), B(0, 2), C(-2, 0), and D(0, – 2). Then, they move along the dance floor following the translation vector, (0, 4). There they pause, and then move again along the same vector. What are their coordinates after six such translations? а. А(26, 24), В'(24, 6), С'(22, 24), аnd D'(24, 22) b. A'(2, 10), B'(0, 12), C'(-2, 10), and D'(0, 8) c. A'(2, 24), B'(0, 26), C'(-2, 24), and D'(0, 22) d. A(26, 0), B' (24, 2), С'(2, 0), and D'(24, - 2) Name: ID: A
Let v₁ = (1,3,5), v² = (-2, 1, 7) and let P be the plane spanned by v¹ and v². (That is, P = (v1, v2).) Let √3 = (7,7,1). Show that (v1, v2, v³) as follows: First show that is in P. • Next explain why (v1, v2, v3) is a subspace of P. • Next explain why P = (v1, v2) is a subspace of (v1, v2, v3). • Conclude that (v1, v2, v3) is the exact same set as P.
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I Find distance from point A(1,2,1) to the plane containing the three points B(2,2,4), C(-1, -2, -3) & D(0,5,7).
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Determine the image under $(u, v) = (7u, u + 5v) of the following sets: (a) U-axis: (x, y) = (b) v-axis: (x, y) = (c) $(9, 3) (x, y) =

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Verify that {u₁,u₂} is an orthogonal set, and then find the orthogonal projection of y onto Span{₁,₂}. y = 7 3 - 3 2 6 U₁ " To] 0 u₂ - 6 2 3]