Let U= Spana) Finda basis of U.b. LetX = 1O1O1O11Ce a subspace of IR³•Using the basis you found in (a) create a matrixBand use this mortrix to find the coordinatevector 1, afx in terms of subspace of U.

The given subspace of is .To find a basis for .To find the coordinate vector of in terms of…

Answered: Tet U= Span 1 O OH a) Find a basis of…

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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Identify whether the following graph is Eulerian or Hamiltonian. And Why? 5
Tet U= Span 1 O 1 1 a) Find a basis of u. b.) Let 1 O O 1 1 le a subspace of IR³ Using the basis you found in () create a mortés = Band use this mortria, to find the coordinate vertor id, of x interms of subspace of
Q 3: a) i Show that W is a subspace of R*. ii. Find a basis for W. b) and Y = (1,1,0,1). Let W = [(a +c, a + b + 2c, a + c,a- b): a, b,c E R}. Find a basis of R* that contains the vectors X = (1,1,1,1)
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Let W C R" be a subspace and let W- C R" be its orthogonal complement. Let S {u1,..., uk} be an orthogonal basis for W and S' The goal of these exercises is to give two different arguments for the fact that {V1,..., Vi} be an othogonal basis for W-. (*) dim W + dim W- = n. 4. Show that SUS' is an orthogonal basis for R" and deduce (*).
In each part, find a basis for the given subspace of R', and state its dimension. a) All vectors of the form (a, b, 0, d). b) All vectors of the form (a, b, c, d) where a = b+d and c= 26 – d. c) All vectors of the form (a, b, c, d) where a = 26 = -c = 3d.
Q15 Please provide justified answer asap to get a upvote
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Let V₁ = ,V₂ = 1 and let W be the subspace of R¹ spanned by V₁ and v2. (a) Convert {V1, V2} into an orhonormal basis of W NOTE: If your answer involves square roots, leave them unevaluated. Basis = {}. (b) Find the projection of b = 1 onto W (c) Find two linearly independent vectors in R¹ perpendicular to W. Vectors = { Note: You can earn partial credit on this problem.
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Tet U= Span 1 O OH a) Find a basis of u. b. Let O 1 1 H 1 1 le a subspace of IR ³ •Using the basis you found in (a) create a matrix Band use this moitrix to find the coordinate vector, 1, of x interms of subspace of U.