Determine whether the vectors w₁ = [2,1,–3], w₁ = [4,0,2], and w3 = [2,−1,3] form a basis for thesubspace sp(w₁,w₂,w₁) in R³.

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Answered: Determine whether the vectors w₁ =…

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 B be the standard basis of the space P₂ of polynomials. Use coordinate vectors to test whether the following set of polynomials span P2. Justify your conclusion. - 5t+t², 1+5t-t²2, 2+t+t², +8t-3t² G Does the set of polynomials span P₂? O A. Yes; since the matrix whose columns are the B-coordinate vectors of each polynomial has a pivot position in each row, the set of coordinate vectors spans R². By isomorphism between R² and P2, the set of polynomials spans P2. O B. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R³. By isomorphism between R³ and P2, the set of polynomials does not span P2. OC. No; since the matrix whose columns are the B-coordinate vectors of each polynomial does not have a pivot position in each row, the set of coordinate vectors does not span R². By isomorphism between R² and P2, the set of polynomials does not span P2. ⒸD. Yes; since the…
Let A = {d1, d,}, B= {B, 6} be two bases of a vector space V. Suppose that 5 b1+7b; Let also 1 Then the change-of-coordinates matrix PA-B from the basis A to the basis B and [x]a are given by:
Explain why S is not a basis for R2. S = {(2, 5), (6, 15)} O sis linearly dependent. O S does not span R2. O is linearly dependent and does not span R2.
2- Show whether the set of vectors S={ ,,} is a basis of R3 ?
(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?
Let H = span {(-13, –1, –3), (-9, 2, -2),(-1,–5,0)}. A basis for the subspace H C R³ is { }. vector
Find a basis for the subspace of R° that is spanned by the vectors V1 = (1,0, 0), v2 = (1, 0, 1), v3 = (2, 0, 1), v4 = (0, 0, -2) Vị and v2 form a basis for span {V1, V2, V3, V4}. V1 and v3 form a basis for span {v1, V2, V3, V4}. V2 and v4 form a basis for span {v1, V2, V3, V43. V1 and v4 form a basis for span {v1, V2, V3, V4}. V2 and v3 form a basis for span {v1, V2, V3, V43. V3 and v4 form a basis for span {v1, V2, V3, V4}. O All of the above are correct.

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Determine whether the vectors w₁ = [2,1,–3], w₁ = [4,0,2], and w3 = [2,-1,3] form a basis for the subspace sp(w₁,w₂,w) in R³.