The set containing the elements specified also possesses its relevant operations ofmultiplication over reals and vector addition. Is the set a real vector space? If possible express the vector v as a linear combination ofV1, V2, and V3.(b) v = (0, 0, -1), V₁ = (2, -1, 1),V3 = (1,-1,0)V₂ = (1, 0, 1),

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Answered: f possible express the vector v as a…

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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Write each vector as a linear combination of the vectors in S. (If not possible, enter IMPOSSIBLE.) S = {(2, 1, 3), (5, 0,4)} (a) Z = Z = V = (b) v-(18,-) 4 W = = (1, -3, 5) (d) (c) w = (4, -7, 13) U= V= ) ₁₁ + ( [ 59 50) u =(3, 1, -1) + )5₁ + (
determine if the following pair of vectors is linearly dependent or linearly independent. show all work (3,5,6) (6,4,11) (-3,-5,6). this is vectors DO IT THIS WAY NOT THE MATRIX OTHER WAY start by making the equation like (-3,-5,6)=a (3,5,6)+ b(6,4,11)
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Show that the column vectors (1,1,2,4), (2,-1,-5,2). (1,-1,-4,0and (2,1,1,6) vectors in R are linearly dependent.
Find the vector in R from point A = (5,4, –6) to B = (-6, 1, 9). | AB help (vectors) %3D
5 Decide the dependence or independence of (a) the vectors (1, 3, 2) and (2, 1, 3) and (3,2,1) (b) the vectors (1, −3, 2) and (2, 1, −3) and (−3, 2, 1).
Vector u has POSITIVE x-component, POSITIVE y-component and ZERO z-component. Vector v has NEGATIVE x-component, POSITIVE y-component and POSITIVE z-component. What is true about u x v? There is not enough information to know anything. O It has NEGATIVE x-component, NEGATIVE y-component, NEGATIVE z-component O It has POSITIVE×-component, NEGATIVE y-component, NEGATIVE z-component It has POSITIVE x-component, NEGATIVE y-component, POSITIVE z-component
Let S be the set of vectors in R4 (S = {V1, V2, V3, V4, V5}) where, V1 = (1,2, −2, −1) v₂ = (-3, 0, -4,3) V3 = (2, 1, −1, −1) v4 = (-3,3,-9,6) V5 = (3,9,7,-6) Find a subset of S that is a basis for the span(S).
Plz
Part B
Let x be the unit vector parallel to the vector from the point (2, 3, −2) to the point (-6,2,2). Find the vector projection of x onto a line with direction vector of (-7,1,2)

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f possible express the vector v as a linear combination of 1, V2, and V3. b) v = (0, 0, -1), V₁ = (2, -1, 1), V3 = (1,-1,0) V₂ = (1, 0, 1),