1. Let V be the subspace of R' spanned by the vectors --() --()--0-0 1 2 1 V4 3 1 1 1 1 (a) Find a basis of V out of the vectors v1, v2, V3, V4! Express the coordi- nates in this basis the vector, which is not in the basis! (b) What are dim(V), dim(V-)?

1. Let V be the subspace of R' spanned by the vectors --() --()--0-0 1 2 1 V4 3 1 1 1 1 (a) Find a basis of V out of the vectors v1, v2, V3, V4! Express the coordi- nates in this basis the vector, which is not in the basis! (b) What are dim(V), dim(V-)?

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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Question

1.
Let V be the subspace of R' spanned by the vectors
--() --()--0-0
1
2
1
U2
V4
3
1
1
1
(a) Find a basis of V out of the vectors v1, v2, V3, V4! Express the coordi-
nates in this basis the vector, which is not in the basis!
(b) What are dim(V), dim(V-)?

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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 = (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.