please send correct answer for Q39 Which of the following statements are True? Select ALL that apply.O If a set of vectors is linearly independent, then the vectors span the vector spaceO span{(1,0, 0), (0,1, 0)} = span{(1,1,0), (1,2,0),(2,1,0)}O No 3 vectors in P, the vector space of polynomials of degree 3 or less, can span the entire spaceAny 5 vectors in R will span the space

Solution: Given that Which of the followings are true

Answered: Which of the following statements are…

Elementary Linear Algebra (MindTap Course List)

8th Edition

ISBN:9781305658004

Author:Ron Larson

Publisher:Ron Larson

Chapter4: Vector Spaces

Section4.CR: Review Exercises

Problem 78CR: Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set...

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Proof When V is spanned by {v1,v2,...,vk} and one of these vector can be written as a linear combination of the other k1 vectors, prove that the span of these k1 vector is also V.
Proof Prove that if S={v1,v2,,vn} is a basis for a vector space V and c is a nonzero scalar, then the set S1={cv1,cv2,,cvn} is also a basis for V.
Let v1, v2, and v3 be three linearly independent vectors in a vector space V. Is the set {v12v2,2v23v3,3v3v1} linearly dependent or linearly independent? Explain.
Illustrate properties 110 of Theorem 4.2 for u=(2,1,3,6), v=(1,4,0,1), w=(3,0,2,0), c=5, and d=2. THEOREM 4.2Properties of Vector Addition and Scalar Multiplication in Rn. Let u,v, and w be vectors in Rn, and let c and d be scalars. 1. u+v is vector in Rn. Closure under addition 2. u+v=v+u Commutative property of addition 3. (u+v)+w=u+(v+w) Associative property of addition 4. u+0=u Additive identity property 5. u+(u)=0 Additive inverse property 6. cu is a vector in Rn. Closure under scalar multiplication 7. c(u+v)=cu+cv Distributive property 8. (c+d)u=cu+du Distributive property 9. c(du)=(cd)u Associative property of multiplication 10. 1(u)=u Multiplicative identity property
Let u, v, and w be any three vectors from a vector space V. Determine whether the set of vectors {vu,wv,uw} is linearly independent or linearly dependent.
ProofProve in full detail that M2,2, with the standard operations, is a vector space.
Proof Let {v1,v2,...,vn} be a linearly independent set of vectors in a vector space V. Delete the vector vk from this set and prove that the set {v1,v2,...,vk1} cannot span V.
Find a basis for R3 that includes the vector (1,0,2) and (0,1,1).
Let V be the set of all positive real numbers. Determine whether V is a vector space with the operations shown below. x+y=xyAddition cx=xcScalar multiplication If it is, verify each vector space axiom; if it is not, state all vector space axioms that fail.
Take this test to review the material in Chapters 4 and 5. After you are finished, check your work against the answers in the back of the book. Prove that the set of all singular 33 matrices is not a vector space.

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