U26. Is the set of all polynomials with integer coefficients a subspace of the set of all polynomials?7. Prove or disprove: If U1, U2, W are subspaces of V such that U₁ + W = U₂+ W then U₁ = U₂8. Suppose V1, V2, V3, V4 spans V. Prove that the following vectors also spans V01 — 02, 02 — ვ, ვ — 04,04

Problem 6No, the set of all polynomials with integer coefficients is not a subspace of the set of…

Answered: U2 6. Is the set of all polynomials…

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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Let v1=[-2,2,1], v2=[-8,7,4], v3=[-29,25,14], w=[6,6,1] is W in {v1,v2,v3}? how many vectors are in {v1,v2,v3}? How many vectors are in span {v1,v2,v3}? is w in the subspace spanned by {v1,v2,v3}?
Гот -08-0 -3 V = and w = We want to determine by inspection (with minimal computation) if {u, v, w} is linearly dependent or independent. Choose the best answer. Let u = 2 A. The set is linearly dependent because one of the vectors is a scalar multiple of another vector. B. The set is linearly independent because we only have two vectors and they are not scalar multiples of each other. C. The set is linearly dependent because one of the vectors is the zero vector. D. The set is linearly dependent because two of the vectors are the same. E. The set is linearly dependent because the number of vectors in the set is greater than the dimension of the vector space. OF. We cannot easily tell if the set is linearly dependent or linearly independent.
1- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (-3,0,4), (5,-1,2), (1,1,3) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 2- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthonormal basis for R³, then obtain an orthonormal basis from them. Express (3,7,-4) as a linear combination of the orthonormal basis. 3- Determine whether the following sets of vectors are linearly dependent or linearly independent. a) (1,1,0), (0,0,1), (0,1,1) in R³ b) (1,0,0), (2,2,0), (3,3,3) in R³ 4- Verify that the set of vectors (-0.6, 0.8, 0), (0.8, 0.6, 0), (0, 0, 1) form an orthogonal basis for R³, then obtain an orthonormal basis from them. Express (2,3,-4) as a linear combination of the orthonormal basis. 5- Find the coordinates of the vector u = (0,25, 1) with respect to the orthogonal basis v₁ = ( 3,4,0), V₂ = (−4, 3, 0 ) and v₂ = (−4,3,0) 6- Find the coordinates of the vector U = (7,5,2) with respect to the basis V₁ =…

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