Basis for an Orthogonal Complement- Let W be the subspace of R$ spanned by the vectors w,=(2, 2,-1, 0, 1), w,=(-1, -1, 2, -3, 1), w;=(1, 1, -2, 0, -1), w,=(0, 0, 1,1, 1). Find a basis for the orthogonal complement of W.22 -1 01-1 -1A =1-311-2-10 111

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Answered: Let W be the subspace of R$ spanned by…

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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Find a basis for the subspace of R° that is spanned by the vectors V1 = (1, 0, 0), v2 = (1, 0, 1), v3 = (5, 0, 1), v4 = (0, 0, -2) V2 and v4 form a basis for span {v1, V2, V3, V4}. V1 and v4 form a basis for span {v1, V2, V3, V4}. V1 and v3 form a basis for span {v1, V2, V3, V4}. Ov1 and v2 form a basis for span {v1, V2, V3, V4}. V2 and v3 form a basis for span {v1, V2, V3, V4}. V3 and v4 form a basis for span {v1, V2, V3, V4}.
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Find a basis for the orthogonal complement of the subspace of Rª spanned by the following vectors. V1 = (1,-1,7,3), V2 = (2,-1,5,2), V3 = (1, 0, -2, -1) The required basis can be written in the form {(x, y, 1, 0), (z, w, 0, 1)}.
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Consider the subspace S of the Euclidean inner product space R+ spanned by the vectors v₁ = (1,1,1,1), v₂=(1,1,2,4), v₂=(1,2,-4,-3). Find an orthogonal basis of S. O*((-.-3.1).(1.2.-4,-3).(4,2,1,1)) OB. © ³ {(1,1,2,4), ( − 1, − 1,0,2 A. -1,0,2), (12. 2.-3,1)} O C. None in the given list. OD. {(1,1,1,1),(1,1,2,4), (1,2,-4,-3) } OE {(1,1,1,1),(-1,-1,0,2), (1,3, -6,2) }
I know the basis converted to orthogonal is {<2, 1, -1, 1>,<11, -12, 5, -5>,<-1, -3, 0, 5>} and that the magnitude of these will be sqrt(7), sqrt(315), sqrt(35) - but I'm not sure how to use these to convert the basis to orthonormal.
(3,0,0), v2 = (1,2,0), and v3 = a) Are the vectors linearly independent or linearly dependent? Given vectors v, = (2, –4,5). b) Do the vectors form a basis for R3? Why or why not?
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Let U and W be subspaces of R*; U=span{(1,1,0,-1), (1,2,2,-2), (1,2,3,0)} and W=span{(2,3,3,-1), (2,3,2,-3), (1,3,4,-3)}. Find a basis for U+W and dim(U+W).

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Let W be the subspace of R$ spanned by the vectors w,=(2, 2, -1, 0, 1), w2=(-1, -1, 2, -3, 1), w3=(1, 1, -2, 0, -1), w,-(0, 0, 1, 1, 1). Find a basis for the orthogonal complement of W.