(c) If we let the basis B = {V₁, V2, V3}, what is [Projw (3, 3, 3, 3)]B, that is, the coordinatesof the projection of (3,3,3,3) onto W with respect to the basis B?(d) What is a basis for W-? 3. Let W1 =(1, 1, 0, 1), w₂ = (−1, 1, 0, 0), w3 = = (1, 2,0,0). Let W = Span(w₁, W2, W3(a) Use the Gram-Schmidt process to obtain an orthogonal basis {V₁, V2, V3} for W.(b) What is Projw (3, 3, 3, 3), the orthogonal projection of the vector (3,3,3,3) onto W?

Using the Gram Schmidt orthogonal process:

Answered: (c) If we let the basis B = {V₁, V2,…

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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(1) Consider the basis 8-{(:) (:)} B = of R2. What is the coordinate vector of (;) with respect to B.
just b)
The coordinates for the vector v = (1,2,4) relative to the standard basis B = {(1,0,0), (0, 1,0), (0,0,1)} is [v] B = (1,2,4). The coordinates for v relative to the nonstandard basis B' = {(1, 0, -1), (2,1,-1), (-2, 1,4)} is [v]B¹ = (9,−1,3). Find the transition matrix P-1 from B to B' and show that this does change the coordinate of v relative to B to the coordinate of v relative to B'.
4. Vector u is a unit vector orthogonal to vectors a and b, where a = i+j-k, b=2i-j. Then the coordinates of vector u in the basis {i, j,k} are 2 3 (a) (b) (-1, 2,–3) (c) None of the above is true
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1 V2 = 2 V3 = 1 Let V1 = V4 = -1 7 For what of value of t is the set {V1, V2, V3, V4 NOT a basis for IR*?
: Let S = {v1, v2}, where v = standard vectors when added to the set S produces a basis for R? (6,-5, 7,-1) and v2 = (-12, 20, -28, 4). Which of the following combination of (A) v3 = (1, 0, 0, 0), v4 = (0, 0, 1, 0) and vs = (0, 0, 0, 1) (B) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0, 0, 0, 1) (C) v3 = (1, 0, 0, 0) and v4 = (0, 0, 0, 1) (D) v3 = (1, 0, 0, 0), v4 = (0, 1, 0, 0) and vs = (0. 0, 1, 0) (E)v3 = (1, 0, 0, 0) and v4 = (0, 1, 0, 0) (F) v3 = (1, 0, 0, 0) and v4 = (0, 0, 1, 0) (G) v3 = (0, 1, 0, 0) and v4 = (0, 0, 0, 1) %3D %3D (H) v3 = (0, 1, 0, 0), v4 = (0, 0, 1, 0) and vs = (0. 0, 0, 1) %3D

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(c) If we let the basis B = {V₁, V2, V3}, what is [Projw (3,3,3,3)]µ, that is, the coordinates of the projection of (3,3,3,3) onto W with respect to the basis B? (d) What is a basis for W-?