3) Suppose that B =for spacevectorکردار کوU2isan orthonormal basis for theV. If x is a vector in v with uz X = -12 andU₂ ·x=91The length of the vector is

Orthonormal basis for the vector space V.We know any vector x in V can be written as

Answered: O that B = 3 U₂₁ U₂ ) is an orthonormal…

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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5. Find the orthogonal projection of the vector b = vectors V₁ = -1- and v2 = onto the subpace E spanned by the (Note that v₁ V₂).
Which of the following sets forms a basis for the vector space given by the plane? — 26х — 32у — 282 %3D 0 {(:)(} "{()} {(:)( {( -2 2 I. -5 5 -26 II. -32 -28 16 III. -6 -8 -2 6 IV. -5 А. II., IV. only В. П, II, only. C. None of the above. D. I, III, only. Е. I, II, only.
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
-13/27] -4/27 -4/9 5/9 -20/27] -2/27 Let v₁ = √2 = and √3 = Find a vector in IR4 such that -20/27 ' ' -2/9 17/27 4/9 -2/3 2/9 {1, 2, 3, 4} is an orthonormal set. Answer:
7. Let V be a vector space and suppose B = {u, v} is a basis for V. Prove that B' = {ku, v} is also a basis for V for every nonzero scalar k. (Hint: You must prove that B'is linearly independent and that it spans V).
2. In a vector space V with inner product (,), the vectors u and v are orthogonal and ||u|| ||v|| = 5. Determine the value of (u + 3v, 2u - 4v). = 3 and

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O that B = 3 U₂₁ U₂ ) is an orthonormal basis t U2 V. If x is a vector in v with uz •X == Suppose vector space U₂ ·x=9/ The length of the vector is